Band offsets at the back contact and front window layer in CdTe-based solar cells affect photovoltaic performance and challenge standard characterization methods. By analyzing the temperature and excitation dependence of both open circuit voltage and absolute photoluminescence intensity, we show that the effects band offsets can be separated from the effects of recombination and shunting. Solar cells were grown with MgZnO window layers and compared to cells with CdS window layers containing varying amounts of oxygen. It was demonstrated that band alignment rather than reduced recombination velocity is the reason for the success of MgZnO as a front interface contact. An assortment of thin back contact interlayers were also deposited, and a PbTe interlayer showed some promise as an Ohmic contact to the CdTe, though it appears to induce a photoconductive shunt. Finally, we show that the shunting resistance given by a standard current-voltage curve technique generally does not represent a physically meaningful quantity unless it is well below one kiloOhm square cm.