Here we report on combined linear and nonlinear magneto-optical studies of Co/garnet heterostructures. Both the crystallographic symmetry and the magnetization of buried Co/garnet interfaces were deduced from an analysis of the rotational anisotropy of spectroscopic magnetization-induced second-harmonic generation (MSHG) measured in the transverse (Voigt) geometry. Unexpected non-zero components of the magnetic MSHG tensor were found, that do not correspond to the original 4mm point group symmetry of (001)-plane oriented garnet layers. They may be tentatively assigned to the anisotropic distribution of the Co impurities. For Co/garnet interfaces, the magnetic MSHG contrast shows a maximum at the fundamental wavelength of about 890 nm which can be correlated with Faraday rotation spectra at the second harmonic frequency. (C) 2014 Elsevier B.V. All rights reserved.