The miscibility behaviour of blends A/alpha-beta of a homopolymer A and a symmetric two-block copolymer-alpha-beta, where the chains A and the blocks-alpha are chemically the same and immiscible with the blocks-beta, is analysed theoretically and experimentally. The blends are compared with corresponding blends A/alpha-beta', where the copolymer-alpha-beta' is random. The styrene (S)/methyl methacrylate (MMA) model systems investigated consist of a copolymer P(S-b-MMA) (two-block) or P(S-co-MMA) (random) and a homopolymer PMMA of varying chain length. The process of phase separation during film casting at different temperatures was analysed by mean-field calculations, and the morphologies of the cast films were studied by transmission electron microscopy. The block copolymer blends exhibit both microphase and macrophase separation, which develop in two steps in the order microphase-macrophase or macrophase-microphase. Which sequence is preferred can be predicted from the homopolymer-copolymer chain-length ratio.