The optical properties of strongly absorbing orthorhombic (and higher-symmetry, uniaxial) crystals are considered. Expressions for the amplitude reflection and transmission coefficients of crystal plates with smooth surfaces parallel to principal planes are presented. Equations for the reflectance and transmittance of crystal layers with rough surfaces are also derived. The expressions are presented in a form that facilitates their computational implementation and their ready comparison with the known formulas corresponding to films of isotropic media. A quantitative description of the contribution to the TM-polarized, off-axis infrared absorption spectrum of anisotropic crystal plates due to polar longitudinal-optic modes will be given. The practical interest of the derived equations for their applications in absorption spectroscopy of solids is emphasized.