We adopted an existing formalism and modified it to simulate, with high precision, the transmission, reflection, and absorption of multiple-plate birefringent devices as a function of frequency. To validate the model, we use it to compare the measured properties of an achromatic five-plate device with a broadband antireflection coating to expectations derived from the material optical constants and its geometric configuration. The half-wave plate presented here is observed to perform well with a phase shift variation of <2° from the ideal 180° over a bandwidth of \Delta \nu /\nu \sim 1 at millimeter wavelengths. This formalism represents a powerful design tool for birefringent polarization modulators and enables its optical properties to be specified with high accuracy.