The reflection coefficient of a plane monochromatic wave from a three-layer structure is analyzed in detail in the case in which the wave is linearly polarized in the plane of incidence. The inverse ellipsometry problem for a three-layer structure is solved. The occurrence of two invariants of the reflection coefficient for a plane-parallel plate is shown. A set of three measurable parameters is proposed, which have not been used previously, that make it possible to retrieve the material parameters of the layer. Analytical expressions are obtained for the reflection coefficient and the angles of incidence for a number of important particular cases, as well as for the direct calculation of the dielectric permittivity and the layer thickness from the measured values of the observed parameters.