The lattice cluster theory (LCT) is used to determine the essential microscopic parameters that influence the phase separation in binary blends of linear semiflexible lattice chains with equal polymerization indices. The LCT and the polymer reference interaction site model are shown to predict nearly identical and universal constant volume phase behaviors (after simple numerical rescaling of the polymerization indices) for "athermal" blends with vanishing van der Waals attractive energies. Phase separation in these systems is driven solely by stiffness disparities. LCT computations are extended to "thermal" systems in which the van der Waals interactions are large enough to produce liquid densities at standard temperature and pressure. Both the stiffness disparity between the blend components and the relative magnitudes of the van der Waals interaction energies influence the phase behavior of the model blends. We find a family of universal constant volume spinodals, parameterized by the exchange energy. Compressibility is shown to produce significant enthalpic contributions to phase separation, even when all van der Waals energies are identical. We also study the pressure dependence of these model blends, as well as the variety of qualitatively different phase behaviors exhibited. A future work will determine the combined influence of monomer structure, semiflexibility, van der Waals interactions, and the energetic implications of compressibility on the phase behavior of polyolefin blends.