An extended form of a Hubbard-like Hamiltonian, which includes electron-electron correlations within a spin unrestricted Hartree-Fock approximation, was used in order to study the electronic properties of dangling bond defects near non-periodic interfaces between Si and SiO2. These are modelled by a cluster of Bethe lattices, as used previously for the (111)-Si/SiO2 interface [R.A. Barrio, R.J. Elliott and A.S. Carrico, Phys. Rev. B34 (1986) 879]. This model is applied to simulate the (110)-Si/SiO2 and (100)-Si/SiO2 interfaces.