A detailed study of the electronic structure of a number of (111) vacuum-semiconductor, metal-semiconductor, and semiconductor-semiconductor interfaces has been made by using a cluster-Bethe-lattice method. Numerical calculations for the electronic density of states of Ge, GaAs, and ZnSe surfaces and interfaces have been performed using a realistic Hamiltonian considering all the nearest-neighbor interactions. The results are in good agreement with those of the earlier self-consistent pseudopotential and the tight-binding calculations. A striking difference is that no true interface states (states lying in the mutual gap) are seen in the Ge-GaAs and Ge-ZnSe (111) interfaces.