  We consider an interface between two demixed A and B phases, confined in a
thin film between two antisymmetric walls, one of which prefers A and the other
B. Above the wetting transition, the interface is stabilized in the center of
the film. Based on a suitable extension of the Cahn-Hilliard gradient-square
theory in combination with the capillary wave theory, we argue that the
confinement influences the interfacial structure in two ways: It squeezes the
intrinsic structure and cuts off the capillary wave spectrum. As a result, the
interfacial width is proportional to the film thickness D in very thin films,
and proportional to the square root of D in thicker films. These effects are
then discussed in detail for the special case of an interface between demixed
homopolymer phases. The width of the intrinsic profile is calculated
analytically as a function of film thickness in the Cahn-Hilliard approximation
(weak segregation limit) and in the Helfand theory (strong segregation limit),
and numerically in the self-consistent field approximation. The results are
confirmed by Monte Carlo simulations of a lattice model for a polymer mixture.
