Electromagnetic wave propagation through materials that possess both Faraday rotation and birefringence is analyzed. A matrix equation is developed which relates the amplitude and relative phase of the electric vectors between any two points along the propagation direction. It is shown that the presence of birefringence can drastically affect the behavior of wave propagation and that it is considerably different from pure Faraday rotation. Methods of measuring the material parameters are also described. Criteria for viewing domains in this type of material are established. It is shown that the thickness of the sample plays a great role in determining the contrast between domains and at some thicknesses no contrast at all can be obtained. It is also shown that the method using elliptical analyzers gives greater contrast over the plane analyzers. Photographs of domain patterns in a wedge of ytterbium orthoferrite are presented and they verify the calculated results.