We present a theoretical investigation of the Goos-H€anchen effect upon light reflection from a heterostructure consisting of an electro-optic film deposited on a magneto-electric film grown on a nonmagnetic dielectric substrate. It is shown that the linear magneto-electric interaction leads to an increase of the lateral shift even in the absence of any applied electric field. The presence of the electro-optic layer enables the control of the Goos-H€anchen shift and of the position of its maximum (with respect to the angle of incidence) through a variation of the magnitude and orientation of an applied electric field. It is also demonstrated that applying an external magnetic field in order to reverse the magnetization in the magnetic layer results (under the influence of the magnetoelectric interaction in the system) in a sign reversal of the lateral shift but a nonreciprocal change of its amplitude.

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