The viscous damping of progressive, two-layer interfacial waves is examined theoretically and experimentally. Traditional water wave theory is modified to derive the damping rates associated with interfacial wave propagation in a rectangular channel. The individual wave damping contributions are considered from the bottom, side, and interfacial boundary layers, as well as the damping associated with the wave-induced velocities within the homogenous fluid layers. These results show that for most laboratory-scale experiments, sidewall friction plays the dominant role in wave damping. Laboratory experiments are conducted to verify the damping rates for progressive two-layer internal waves in a rectangular channel. Experiments are conducted on both monochromatic and polychromatic wave trains. The results of these experiments are in good agreement with the derived damping rates, but show poorer agreement for large-amplitude waves when the sidewall boundary layers become turbulent. More work is necessary to quantify the damping associated with nonlinear internal waves in order to allow for accurate interpretation of the results from laboratory experiments.