The properties of the low frequency surface waves in inhomogeneous, magnetized collisional complex dusty plasma are investigated in this work. The inhomogeneity is modelled by the two distinct regions of the dusty medium with different dust densities. The external magnetic field is assumed to be oriented along the interface dividing the two medium. It is shown that the collisional momentum exchange that is responsible for the relative drift between the plasma particles affects the propagation of the surface waves in the complex plasma via the Hall drift of the magnetic fluctuations. The propagation properties of the sausage and kink waves depend not only on the grain charge and size distribution but also on the ambient plasma thermal conditions.