I haven't seen any announced plans to have one HQ focus on one of the three businesses and the other on another, but that would make at least a bit more sense. But then, what about the third business?
If I had to guess I'd say the decision to keep both the headquarters is psychology-driven. You don't want either the Dow folks or the DuPont folks thinking that they're the target, because usually in M&A situations the acquiror keeps A LOT more of its corporate overhead. So logically, this perhaps makes the most sense as an attempt to avert the desertion of a lot of talented lawyers, accountants, HR people, and other headquarters types.
If that is in fact the case, expect an announcement about six months after the deal closes that they're consolidating their headquarters. My guess is they'd keep it in Delaware.