looking at the latest aerial (geoportal 2) i can clearly see a white hashed area indicating a divided highway  (look at where the roads diverge/converge) there are turn lanes which complicate classifying it but as far as i know there is know way to add a dedicated turn lane in OSM. 
As such I think a divided highway with the crossovers (as it is) is the best way to show this area. (I might be wrong tho im pretty new to this)