Comparison of the Biot theory with experimental results over a broad range of frequencies has proven to be difficult because the coefficients in Biot's equations are functions of frequency whose forms depend upon the microstructure of the medium. In this work, Biot's equations are used to analyze the propagation of plane waves parallel to the layers of a laminated material consisting of alternating layers of an elastic material and a compressible viscous fluid. For this case, all of the coefficients in the theory can be evaluated. In particular, the drag and virtual mass coefficients can be evaluated as functions of frequency using the method of Bedford, Stern, and Costley [J. Acoust. Soc. Am. Suppl. 174, S57 (1983)]. Furthermore, the phase velocity and attenuation of plane waves in the layered medium can be determined exactly. Although it is for a special geometry, this comparison provides a definitive test of the ability of the Biot theory to model a two‐phase material. It is shown that the Biot theory matches the first two modes of the exact results with great accuracy over a large range of frequency. However, this result is shown to depend upon the use of an appropriate frequency‐dependent expression for the virtual mass coefficient.