What does Classic Dispensationalism teach about the eternal state?

I've been learning about the various flavors of dispensational and covenant theology. Classic Dispensationalism (as taught by Darby, Scofield, Ryrie, etc) holds that God plans to bring literal fulfillment to Old Testament prophecies about the physical kingdom of Israel during the Millennium, and that the church does not share in these promises. (I do not agree with this view for various reasons, but am trying to understand it the best that I can.) One thing I have not understood, though: according to that system, do Israel and the church remain separate forever, or are they finally merged after the Millennium? What does Classic Dispensationalism say about the relationship between Israel and the church in the eternal state?