A longitudinal magneto-optical Kerr effect and magnetization-induced second-harmonic generation (MSHG) of light (at 2v) have been measured in a SiO2/Fe96Si4/Dy30Fe58Co12/glass exchange-coupled magnetic bilayer system with competitive anisotropies. Theoretical MSHG predictions in this structure that give rise to an effect proportional to magnetization components and that are allowed by an electric dipole mechanism are reported and discussed. The magnitude of the MSHG effect depends on the electric field of the incoming radiation at each interface and on the corresponding incoming (at v) and outgoing (at 2v) Fresnel coefficients. It is demonstrated that transverse pp MSHG selectively probes the magnetization of the first SiO2/Fe96Si4 interface, while transverse sp and longitudinal ps MSHG is sensitive, but less selectively, to the Fe96Si4/Dy30Fe58Co12 interface that supports a planar magnetic domain wall. (p and s are the usual parallel and perpendicular polarizations to the plane of incidence.) The contribution to MSHG by gradient magnetization terms is negligible