A self-consistent field model is used to study the effect of mixing on self-assembled diblock copolymer monolayers and bilayers, in the strong segregation limit. The mixtures contain chains of identical chemistry but different molecular weights or asymmetries. The interactions between such chains are shown to be attractive, so that segregation is unfavorable. The equilibrium curvature and surface density of the monolayer vary nonlinearly with mixture composition, due to interactions between the components. In bilayers, the spontaneous curvature energy promotes demixing, i.e., nonuniform distribution of the components between the two monolayers composing the bilayer. While a homogeneously mixed system adopts a lamellar configuration, in the demixed bilayer equilibrium vesicles are favorable. The stability boundaries of the lamellar, vesicular, and saddle-shaped phases are calculated as a function of chain characteristics and mixture composition.