We report on a type of Si interband transitions at ${\mathrm{Si}(100)\ensuremath{-}\mathrm{S}\mathrm{i}\mathrm{O}}_{2}$ interfaces that has no equivalent in the bulk of crystalline silicon. These transitions, leading to strong resonances in optical second-harmonic-generation spectra with energies of 3.6\char21{}3.8 eV, are energetically located between the ${E}_{1}$ and ${E}_{2}$ critical points of bulk Si. We assign these transitions to Si atoms without ${T}_{d}$ lattice symmetry at the boundary between crystalline Si and the ${\mathrm{SiO}}_{x}$ transition region. We also report on a strong blueshift of the ${E}_{2}$ transitions at the interface.