We show that the anisotropies of second-harmonic-generation (SHG) intensities, of singular and vicinal (111) and (001) Si-dielectric interfaces can be described accurately as dipole radiation originating from the anharmonic motion of bond charges parallel to the bond directions. This simplified bond-hyperpolarizability model not only provides a simpler and mathematically more efficient representation of SHG, but also allows a direct physical interpretation at the bond level, which was lacking in previous approaches. Application to oxidized and nitrided Si-SiO2 interfaces provides new insight into bonding that occurs at these interfaces as well as the origin of SHG.