<PAGE>   1
                                       Registration Statement No.333-


                        SECURITY AND EXCHANGE COMMISSION
                             Washington, D.C. 20549


                                    FORM S-8
                          REGISTRATION STATEMENT UNDER
                           THE SECURITIES ACT OF 1933


                         Intermedia Communications Inc.
             ------------------------------------------------------
             (Exact name of registrant as specified in its charter)


          Delaware                                   59-2913586
-------------------------------                 -------------------
(State or other jurisdiction of                  (I.R.S. Employer
 incorporation or organization)                 Identification No.)


                  One Intermedia Way, Tampa, Florida 33647-1752
                  ---------------------------------------------
                    (Address of principal executive offices)


             Intermedia Communications Inc. Long-Term Incentive Plan
             -------------------------------------------------------
                            (Full title of the plan)

                                 David C. Ruberg
                        Chairman of the Board, President
                           And Chief Executive Officer
                         Intermedia Communications Inc.
                               One Intermedia Way
                              Tampa, FL 33647-1752
                     ---------------------------------------
                     (Name and address of agent for service)

                                  (813)829-0011
          -------------------------------------------------------------
          (Telephone number, including area code, of agent for service)

                                 with a copy to:
                            Ralph J. Sutcliffe, Esq.
                        Kronish Lieb Weiner & Hellman LLP
                           1114 Avenue of the Americas
                          New York, New York 10036-7798
                                 (212) 479-6170




<PAGE>   2

                         CALCULATION OF REGISTRATION FEE

<TABLE>
<CAPTION>

Title of Securities to be      Amount to be          Maximum           Maximum Aggregate       Amount of
Registered                     Registered            Offering Price    Offering Price          Registration Fee
                               (1)                   Per
                                                     Share(2)
---------------------------------------------------------------------------------------------------------------
<S>                            <C>                   <C>               <C>                     <C>
Common Stock,
par value $.01
per share                       3,750,000              $33.0625          $123,984,375             $32,731
</TABLE>

(1) This registration statement also pertains to rights to purchase one unit
consisting of one one-thousandth of one share of Series A Preferred Stock
("Rights") of the Registrant. Upon the occurrence of certain prescribed events,
one Right will be issued for each share of Common Stock. Until the occurrence of
such events, the Rights are not exercisable, will be evidenced by ownership of
the Common Stock and will be transferred along with and only with the Common
Stock.

(2) Average of the high and low prices of Common Stock as reported on the Nasdaq
National Market on June 12, 2000, pursuant to Rule 457 (h) (1).










                                       2
<PAGE>   3


                                     PART II
               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

         The contents of the Registration Statement on Form S-8 (File No.
333-03955) of Intermedia Communications Inc. (f/k/a Intermedia Communications of
Florida, Inc.) are incorporated by reference.

         All documents subsequently filed by the Company with the SEC pursuant
to Sections 13(a), 13(c), 14 and 15(d) of the Exchange Act, prior to the filing
of a post-effective amendment which indicates that all securities registered
have been sold or which deregisters all securities then remaining unsold, shall
be deemed to be incorporated by reference in this Registration Statement and to
be a part hereof from the date of filing of such documents.

Item 5.  Interests of Named Experts and Counsel

         Ralph J. Sutcliffe, a partner of Kronish Lieb Weiner & Hellman LLP,
beneficially owns 11,490 shares of the Company's common stock, par value $.01
per share, a warrant to purchase 200,000 shares of the Company's common stock at
an exercise price equal to $20.75 per share, and subject to vesting, options to
purchase 22,000 shares of the Company's common stock at an exercise price of
$34.1875 per share. Mr. Sutcliffe is a director of the Company.



















                                       3
<PAGE>   4

Item 8.  Exhibits

Exhibit
Number                              Exhibit
-------                             -------

5.1      Opinion of counsel as to legality of the shares of common stock
         covered by this Registration Statement

23.1     Consent of independent auditors
23.2     Consent of counsel (included within Exhibit 5.1)

24.1     Power of Attorney (see signature page)

--------------



















                                       4
<PAGE>   5


                                   SIGNATURES

         Pursuant to the requirements of the Securities Act of 1933, the
Registrant certifies that it has reasonable grounds to believe it meets all the
requirements for filing on Form S-8 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Tampa, State of Florida, on this 13 day of June,
2000.


                            Intermedia Communications Inc.


                            By: /s/ Robert M. Manning
                                ---------------------------
                            Robert M. Manning,
                            Senior Vice President and Chief
                            Financial Officer

         Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities and on the dates indicated. Each person whose signature appears below
authorizes David C. Ruberg and Robert M. Manning, or either of them, as
attorney-in-fact to sign and file in each capacity stated below, all amendments
and post-effective amendments to this Registration Statement.

         Signature                           Title                    Date
         ---------                           -----                    ----

Principal Executive Officer:

/s/  David C. Ruberg               Chairman of the Board          June 13, 2000
----------------------------       President, and Chief
     David C. Ruberg               Executive Officer

Principal Financial and
Accounting Officers:

/s/  Robert M. Manning             Senior Vice President and      June 13, 2000
---------------------------        Chief Financial Officer
     Robert M. Manning

/s/  Jeanne M. Walters             Vice President, Controller     June 13, 2000
---------------------------        And Chief Accounting
     Jeanne M. Walters             Officer

Other Directors:

/s/  John C. Baker                 Director                       June 13, 2000
---------------------------
     John C. Baker

                                   Director                       June   , 2000
---------------------------

     Philip A. Campbell




                                       5
<PAGE>   6

/s/  George F. Knapp               Director                       June 13, 2000
---------------------------
     George F. Knapp

/s/  James H. Greene, Jr.          Director                       June 13, 2000
---------------------------
     James H. Greene, Jr.

/s/  Alexander Navab               Director                       June 13, 2000
---------------------------
     Alexander Navab

/s/  Ralph J. Sutcliffe            Director                       June 13, 2000
---------------------------
     Ralph J. Sutcliffe




                                        6
<PAGE>   7

                                  EXHIBIT INDEX

Exhibit
Number                              Exhibit                                Page
-------                             -------                                ----
5.1               Opinion of counsel as to legality of the shares
                  of common stock covered by this Registration
                  Statement
23.1              Consent of independent auditors
23.2              Consent of counsel (included within Exhibit 5.1)
24.1              Power of Attorney (see signature page)























                                       7
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{"company-data": {"conformed-name": "INTERMEDIA COMMUNICATIONS INC", "cik": "0000885067", "assigned-sic": "4813", "irs-number": "592913586", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-39312", "film-number": "655262"}, "business-address": {"street1": "3625 QUEEN PALM DR", "street2": "STE 720", "city": "TAMPA", "state": "FL", "zip": "33619", "phone": "8138290011"}, "mail-address": {"street1": "3625 QUEEN PALM DRIVE", "city": "TAMPA", "state": "FL", "zip": "33619-1309"}, "former-company": {"former-conformed-name": "INTERMEDIA COMMUNICATIONS OF FLORIDA INC", "date-changed": "19930328"}}
1
                                       Registration Statement No.333-

                        SECURITY AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM S-8
                          REGISTRATION STATEMENT UNDER
                           THE SECURITIES ACT OF 1933

                         Intermedia Communications Inc.
             ------------------------------------------------------
             (Exact name of registrant as specified in its charter)

          Delaware                                   59-2913586
-------------------------------                 -------------------
(State or other jurisdiction of                  (I.R.S. Employer
 incorporation or organization)                 Identification No.)

                  One Intermedia Way, Tampa, Florida 33647-1752
                  ---------------------------------------------
                    (Address of principal executive offices)

             Intermedia Communications Inc. Long-Term Incentive Plan
             -------------------------------------------------------
                            (Full title of the plan)

                                 David C. Ruberg
                        Chairman of the Board, President
                           And Chief Executive Officer
                         Intermedia Communications Inc.
                               One Intermedia Way
                              Tampa, FL 33647-1752
                     ---------------------------------------
                     (Name and address of agent for service)

                                  (813)829-0011
          -------------------------------------------------------------
          (Telephone number, including area code, of agent for service)

                                 with a copy to:
                            Ralph J. Sutcliffe, Esq.
                        Kronish Lieb Weiner & Hellman LLP
                           1114 Avenue of the Americas
                          New York, New York 10036-7798
                                 (212) 479-6170
2

                         CALCULATION OF REGISTRATION FEE
Title of Securities to be      Amount to be          Maximum           Maximum Aggregate       Amount of
Registered                     Registered            Offering Price    Offering Price          Registration Fee
                               (1)                   Per
                                                     Share(2)
---------------------------------------------------------------------------------------------------------------
Common Stock,
par value $.01
per share                       3,750,000              $33.0625          $123,984,375             $32,731
(1) This registration statement also pertains to rights to purchase one unit
consisting of one one-thousandth of one share of Series A Preferred Stock
("Rights") of the Registrant. Upon the occurrence of certain prescribed events,
one Right will be issued for each share of Common Stock. Until the occurrence of
such events, the Rights are not exercisable, will be evidenced by ownership of
the Common Stock and will be transferred along with and only with the Common
Stock.

(2) Average of the high and low prices of Common Stock as reported on the Nasdaq
National Market on June 12, 2000, pursuant to Rule 457 (h) (1).

                                       2
3

                                     PART II
               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

         The contents of the Registration Statement on Form S-8 (File No.
333-03955) of Intermedia Communications Inc. (f/k/a Intermedia Communications of
Florida, Inc.) are incorporated by reference.

         All documents subsequently filed by the Company with the SEC pursuant
to Sections 13(a), 13(c), 14 and 15(d) of the Exchange Act, prior to the filing
of a post-effective amendment which indicates that all securities registered
have been sold or which deregisters all securities then remaining unsold, shall
be deemed to be incorporated by reference in this Registration Statement and to
be a part hereof from the date of filing of such documents.

Item 5.  Interests of Named Experts and Counsel

         Ralph J. Sutcliffe, a partner of Kronish Lieb Weiner & Hellman LLP,
beneficially owns 11,490 shares of the Company's common stock, par value $.01
per share, a warrant to purchase 200,000 shares of the Company's common stock at
an exercise price equal to $20.75 per share, and subject to vesting, options to
purchase 22,000 shares of the Company's common stock at an exercise price of
$34.1875 per share. Mr. Sutcliffe is a director of the Company.

                                       3
4

Item 8.  Exhibits

Exhibit
Number                              Exhibit
-------                             -------

5.1      Opinion of counsel as to legality of the shares of common stock
         covered by this Registration Statement

23.1     Consent of independent auditors
23.2     Consent of counsel (included within Exhibit 5.1)

24.1     Power of Attorney (see signature page)

--------------

                                       4
5

                                   SIGNATURES

         Pursuant to the requirements of the Securities Act of 1933, the
Registrant certifies that it has reasonable grounds to believe it meets all the
requirements for filing on Form S-8 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Tampa, State of Florida, on this 13 day of June,
2000.

                            Intermedia Communications Inc.

                            By: /s/ Robert M. Manning
                                ---------------------------
                            Robert M. Manning,
                            Senior Vice President and Chief
                            Financial Officer

         Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities and on the dates indicated. Each person whose signature appears below
authorizes David C. Ruberg and Robert M. Manning, or either of them, as
attorney-in-fact to sign and file in each capacity stated below, all amendments
and post-effective amendments to this Registration Statement.

         Signature                           Title                    Date
         ---------                           -----                    ----

Principal Executive Officer:

/s/  David C. Ruberg               Chairman of the Board          June 13, 2000
----------------------------       President, and Chief
     David C. Ruberg               Executive Officer

Principal Financial and
Accounting Officers:

/s/  Robert M. Manning             Senior Vice President and      June 13, 2000
---------------------------        Chief Financial Officer
     Robert M. Manning

/s/  Jeanne M. Walters             Vice President, Controller     June 13, 2000
---------------------------        And Chief Accounting
     Jeanne M. Walters             Officer

Other Directors:

/s/  John C. Baker                 Director                       June 13, 2000
---------------------------
     John C. Baker

                                   Director                       June   , 2000
---------------------------

     Philip A. Campbell

                                       5
6

/s/  George F. Knapp               Director                       June 13, 2000
---------------------------
     George F. Knapp

/s/  James H. Greene, Jr.          Director                       June 13, 2000
---------------------------
     James H. Greene, Jr.

/s/  Alexander Navab               Director                       June 13, 2000
---------------------------
     Alexander Navab

/s/  Ralph J. Sutcliffe            Director                       June 13, 2000
---------------------------
     Ralph J. Sutcliffe

                                        6
7

                                  EXHIBIT INDEX

Exhibit
Number                              Exhibit                                Page
-------                             -------                                ----
5.1               Opinion of counsel as to legality of the shares
                  of common stock covered by this Registration
                  Statement
23.1              Consent of independent auditors
23.2              Consent of counsel (included within Exhibit 5.1)
24.1              Power of Attorney (see signature page)

                                       7