Optical second harmonic generation (SHG) spectra of LaAlO3/SrTiO3, LaGaO3/SrTiO3, and NdGaO3/SrTiO3 interfaces with SrTiO3 substrates have been measured up to 4.2 eV as a function of film thickness and temperature. This spectral range is characterized by two-photon transitions from the valence to conduction bands of SrTiO3 which are classified with a model based on symmetry, selection rules, and atomic orbital overlaps. This model is further confirmed in spectral measurements as a function of film thickness, material overlayer, and temperature. SHG enhancement at low temperature indicates an increase of the interfacial polarity with decreasing temperature. This confirms the relation between SHG and the spatial translation of Ti ions which are more prone to move at lower temperatures because of the quantum-paraelectric nature of SrTiO3. We finally show that SHG spectroscopy captures structural details of the interfaces. In particular, we find evidence for proximity effects such as LaAlO3-induced distortions of the TiO6 octahedra or bond buckling. We also observe a correlation between SHG and the in-plane lattice mismatch between the SrTiO3 substrate and the LaAlO3, LaGaO3, and NdGaO3 overlayers.