The scattering of waves in a two-layer fluid of varying mean depth is examined in a three-dimensional context using linear theory. A variational technique is used to construct a particular type of approximation which has the effect of removing the vertical coordinate and reducing the problem to two coupled partial differential equations in two independent variables. A transformation of this differential equation system leads to a particularly simple approximate representation of the scattering process. The theory is applied to two-dimensional scattering, for which a set of symmetry relations is derived. A selection of numerical results is presented to illustrate the principle interest in the problem, namely the energy transfer between surface and interfacial waves induced by bed undulations.