We experimentally studied the generation of optical second harmonic (SH) and magneto-optical effects at the SH frequency in thin films consisting of ferromagnetic and antiferromagnetic materials, including exchange-bonded layers, one of which is pinned with an antiferromagnetic layer. As expected, the loops of the linear magneto-optical Kerr effect are shifted relative to the zero magnetic field value, which reflects the presence of a pronounced exchange interaction in such structures. It is shown that in the case of the nonlinear Kerr magneto-optical effect this effect is also present, but it is significantly smaller than in the nonlinear case, and leads to the observation of only one hysteresis loop instead of two. The studied dependence of the magneto-optical response at the TH frequency on the probing laser radiation power demonstrates that its growth leads to a decrease in the magnetic hysteresis loop shift of the TH. Keywords: magnetization-induced SHG, ferromagnet/antiferromagnet interface, pinned structure, thin films