The perturbed hard-sphere-chain (PHSC) equation of state for copolymer systems is applied to binary polymer mixtures containing random copolymers. Intersegmental parameters are obtained for several pairs of segments, and theoretical miscibility maps are compared with experiment for systems containing two, three, and four kinds of segments. The PHSC equation of state is able to represent immiscibility caused by lower critical solution temperature (LCST) phase behavior as well as that caused by upper critical solution temperature phase behavior. For the system poly(methyl methacrylate)/poly-(acrylonitrile-co-styrene), theory represents the miscibility window caused by LCST behavior where miscibility changes from immiscible --> miscible --> immiscible as the composition of poly(acrylonitrile-co-styrene) random copolymer becomes rich in acrylonitrile. Using the same set of intersegmental parameters, theoretical miscibility maps and experiment show good agreement for systems containing styrene, acrylonitrile, methyl methacrylate, and cyclohexyl methacrylate.