The strongly segregated lamellar state of blends of a diblock copolymer with a "long" homopolymer that interacts favorably with one of the blocks of the copolymer is analyzed in detail. The main observations concern the parabolic homopolymer distribution profile, the presence of "dead" zones near the block copolymer interface where no homopolymer is present, and the maximal amount of homopolymer that can be dissolved. Essential parameters are the interfacial tension, the length, and composition of the block copolymer and the Flory-Huggins parameter chi < 0 representing the favorable interaction between the homopolymer and one of the blocks of the copolymer. Applications are presented for blends consisting of polystyrene-block-poly(4-vinylpyridine) diblock copolymers and poly(2,6-dimethyl-1,4-diphenyl oxide) homopolymers. If the favorable interaction is too weak, no homopolymer will dissolve at all due to the unfavorable conformational effects accompanying an inhomogeneous homopolymer distribution.