Presents a non-separable one-dimensional two-body problem. It describes the reflection of a two-particle bound state off a discontinuity across which there is a steplike change in the interparticle potential. The model can be used as a primitive description of a pick-up or stripping reaction at an interface and also describes the diffusion of a particle in a plane containing an extended finite depth trap. The reflection coefficient for the discontinuity is obtained in closed form.