The recently developed technique of Raman heterodyne detection has unveiled a new interference effect in the Zeeman spectrum of hyperfine transitions of impurity-ion solids. An earlier theory had been developed to explain the basic Raman heterodyne process which involves the resonant interaction of a three-level quantum system with coherent optical-frequency and radiofrequency fields. However, it was not realized that impurity-ion crystals can generate more than one type of Raman heterodyne signal and that these signals can interfere. This article describes two examples of interference where one originates from two or more inequivalent nuclear sites and the other from a single site that exhibits interference among Zeeman transitions. An analytical theory covering these two cases is presented and compared to observations for the impurity-ion crystals Pr3+:YAlO3 and Pr3+:LaF3, the interference behavior in the two being dramatically different. © 1985 The American Physical Society.