The structure and thermodynamics of the interface between polystyrene (PS) and poly(methyl methacrylate)(PMMA) homopolymers with and without a diblock copolymer (for example, PS–PMMA) are elucidated using the Scheutjens and Fleer self-consistent, mean-field lattice model extended to incorporate conformational stiffness. All parameters of the model are obtained from known properties of the homopolymers, except for the Flory χ interaction parameter, which is fit to the binary interfacial width of 50 Å. Using this χ, volume fraction profiles for the ternary interface match experiment quantitatively, giving an interfacial width of 75 Å. The interfacial width exhibits a weak dependence on characteristic ratio. Although the volume-fraction profiles decay to the bulk values over ca. 200 Å on each side, structural characteristics, such as the end-segment volume fractions and the mean-square z-component of the end-to-end distance, may differ from their bulk values as much as 400 Å away from the interface. The volume-fraction, end-segment, mean-square z-component of the end-to-end distance, shape-parameter and bond-order parameter profiles indicate that copolymer chains are significantly stretched under experimental conditions. For fixed surface density of chains, with increasing chain length, a transition from reflected random coil to brush behaviour occurs over the region where the block radii of gyration are 1.2 to 1.7 times the mean interchain spacing. At high enough volume of copolymer per unit surface, the copolymer can no longer reside in a monolayer. Surface-phase equilibrium calculations between a monolayer and a trilayer predict that patches of trilayer will appear when the volume of copolymer per unit surface is roughly three times the block unperturbed root mean-square radius of gyration. The formation of a trilayer suggests an upper limit to the degree of strengthening of the interface by addition of larger amounts of block copolymer, as seen experimentally.