We study theoretically the temporal evolution and the spatial structure of the interface between two polymer melts involving three different species (A, A*, and B). The first melt is composed of two different polymer species A and A* which are fairly indifferent to one another (Flory parameter chi(AA) 0). The second melt is made of a pure polymer B which is strongly attracted to species A (chi(AB) < 0) but strongly repelled by species A* (chi(A*B) > 0). We then show that, due to these contradictory tendencies, interesting properties arise during the evolution of the interface after the melts are put into contact: as diffusion proceeds, the interface structures into several adjacent "compartments", or layers, of differing chemical compositions, and in addition, the central mixing layer grows in a very asymmetric fashion. Such unusual behavior might lead to interesting mechanical properties and demonstrates in a specific case the potential richness of multicomponent polymer interfaces (as compared to conventional two-component interfaces) for various applications.