The interfacial profile between coexisting phases of a binary mixture (A,B) in a thin film of thickness D and lateral linear dimensions L depends sensitively on both the linear dimensions and on the nature of the boundary conditions and statistical ensembles applied. These phenomena, generic for systems in confined geometry, are demonstrated by Monte Carlo simulations of the bond fluctuation model of symmetric polymer mixtures, using chains containing N-A=N-B=N=32 effective monomers connected by effective bonds with an attractive interaction between monomers of the same type and a repulsive interaction between different types. We use short-range potentials at the walls, the right wall favoring A monomers and the left wall B monomers. Periodic boundary conditions are applied in the directions parallel to the walls. Both the canonical and semi-grand-canonical ensemble are studied. We argue that the latter case is appropriate for experiments with a lateral resolution L much less than the actual lateral sample size, in thermal equilibrium. In the canonical ensemble, the interfacial width w increases (from small values that are of the same order as the ''intrinsic profile'') like w proportional to root D, before a crossover to a saturation value w(max) (w(max)(2) proportional to In L) sets in. In the semi-grand-canonical ensemble, however, one finds the same widths w proportional to root D as in the canonical ensemble for not too large L, while for large L the interfacial profile is smeared out over a finite fraction of the film thickness (w proportional to D for D-->infinity). We discuss the implications of these findings for the interpretation of both simulations and experiments. (C) 1997 American Institute of Physics.