In this paper we discuss the magneto-optical Kerr effect in the frequency doubled light (MSHG, magnetization-induced second harmonic generation) generated at interfaces of ultrathin ferromagnetic films and the surface of crystals having inversion symmetry. We demonstrate that the '`magnetic signals" like the nonlinear Kerr angle or the asymmetry can be strongly affected by the '`nonmagnetic" part of the second-order nonlinear susceptibility tensor, χ(nonmag)((2)). This changes of χ(nonmag)((2)) can be caused by the change of the electronic structure with film thickness (quantum well states in the Cu cover layer of Cu/Co/Cu(0 0 1)) or by changes of the surface morphology. One monolayer (ML) periodic oscillation during the layer-by-layer growth of Co films on Cu(0 0 1) were observed in the magnetic second order susceptibility chi(nonmag)((2)).