The random phase approximation (RPA) and the lattice fluid (LF) model are combined to formulate expressions for scattering, the spinodal, and the interaction parameter from compressible polymer mixtures. Effective fields of the RPA are shown to correspond to the interaction parameters of the LF model A protocol is developed to determine polymer-polymer interaction parameters from scattering data. The formalism is applied successfully to both isotopic and nonisotopic binary polymer blends. It is concluded that some of the unexpected behavior of interaction parameters determined in neutron scattering experiments can be attributed to compressibility effects. The traditional and widely used formula that relates the interaction parameter to a second concentration derivative of an excess free energy is shown to be incorrect for compressible mixtures. Radii of gyration determined from the scattering dependence on wave vector tend to be overestimates unless compressibility is taken into account. It is also shown that the spinodal determined from a scattering experiment that probes a constant volume is identical to one obtained under conditions of constant pressure.