When a light beam impinges on an optical system, the reflected beam can exhibit a lateral shift relatively to the position predicted by geometric optics for ideal light rays|that is the Goos-Hänchen shift (GHS). In magneto-optical materials, the GHS can reach values up to several tens of light wavelengths. Thus, the GHS should be taken into account for the precise design of integrated optical or magneto-optical devices. Furthermore, it is well-known that certain classes of magnetic materials possess magneto-electric (ME) properties, which result in the induction of a magnetization by an electric field or the induction of a dielectric polarization by a magnetic field. It has been shown that the linear ME interaction modifies the complex reflectivity of a magnetic/dielectric bilayer. Thus the ME properties can also be expected to influence the GHS of light reflected from such a system.