We present a study of the electronic and optical properties of CdTe-ZnTe superlattices using an empirical tight-binding approach. We report that a wide-gap strained semiconductor superlattice can support valence-interface states when heavy-hole bands in both materials are almost aligned. We follow the evolution of these unusual states as a function of superlattice period size and valence-band offset. Optical transitions between the lowest-conduction-band and valence-interface states are dominant for short-period superlattices.