The idea is carving out a white homeland and a black homeland from the existing US. This is a geographical partition. Culture is people, and they are free to carry it with them. Yes, nonethnics within the ethnostates would have to leave. Black people probably get DC, if that makes it any more palatable.

People who want to continue to live in a multiethnic society continue to do so in the third state. It's a continuation of the existing US, so by default they keep everything except some territory.

Ideally lines would be drawn to maximize existing enfranchisement. The Pacific Northwest has been discussed as a white homeland. The South has been proposed as a black homeland. Very roughly, that's probably the way it goes. It is, of course, impossible to be fair to everyone -- there will be winners and losers. Proportional land distribution is an option, but it doesn't seem ideal. Perhaps every county could be assigned a value somehow, and some horse trading could occur. Depending on how many people want to continue to comprise the multiethnic United States, that could occupy most of the existing US. I'm guessing Ethnics are more willing to give up cities than Polyglots. I'm not saying it's easy, but the smart money seems to think the US is doomed, so...