The natural frequency of an interface between a bilayer of immiscible fluids is shown to depend on the morphology of the bottom wall in addition to the density difference of the fluids, the interfacial tension, the fluid depths, and the disturbance wave number. To take into account deep wall-wave amplitudes and the viscosities of the fluids, a reduced-order method is employed that assumes the thickness of the bilayer to be small in comparison to the container width.