An analytically tractable, more realistic extension of random copolymer Flory-Huggins (FH) theory Is developed for A(x)B(1-x)/CyD1-y, A(x)B(1-x)/A(y)B(1-y), and A/CyD1-y random copolymer binary blends. The theory describes the polymer-polymer interactions in terms of the interactions between united atom groups and includes a temperature-independent contribution chi(s) to the effective interaction parameter chi. chi(s) is determined (with no adjustable parameters) from the lattice cluster theory in the incompressible, athermal, fully flexible, long-chain limit. The general, readily applied expressions for the interaction parameter chi are illustrated for norbornene-co-ethylene (NxE1-x/NyE1-y) random copolymer mixtures for which the theory has been successfully used by Delfolie et al. (Macromolecules 1999, 32, 7781) to explain miscibility data that depart significantly from the predictions of classic random copolymer FH theory. Further illustrations describe the influence of chain semiflexibility and sequence dependence on the miscibility of NxE1-x/NyE1-y blends. The theory is then applied to isotopic mixtures of saturated poly(butadienes) (sPB) whose randomness stems from the random addition of 1,2 and 1,4 units in the polymerization process. A final application treats blends of ethylene-co-alpha-alkene random copolymers with sPB.