Ultrathin Ni films in Cu/Ni/Cu(001) bilayers and exchange coupled Ni films in Ni/Cu/Ni/Cu(001) trilayers are investigated by magnetization induced second harmonic generation (MSHG). The results are analyzed in a model of localized nonlinear polarizabilities at the interfaces. We show that antiferromagnetic coupling in the Ni/Cu/Ni trilayes is observable with MSHG due to the presence of quantum well states (QWS's) in the Cu layer. The influence of the QWS's on the SHG from a Ni film in a Cu/Ni/Cu(001) bilayer is weaker compared to the case of Fe or Co bilayers.