A steady source-sink driven flow in a rotating annulus is considered. The source and sink are located at the inner and outer cylinder, and consist of two immiscible fluids of different density and viscosity. For an axisymmetric source-sink distribution it is shown that the interior (geostrophic) flow in each layer is the sum of a potential vortex and a solid body rotation. Moreover, the flow in each layer is anticyclonic when the source is located at the inner cylinder, and vice versa. Some aspects of the interfacial stability are also reported.