Continuum-scale equations of radiative transfer and corresponding boundary conditions are derived for a multi-component anisotropic medium consisting of components in the range of geometrical optics. The derivations are obtained by employing the volume-averaging theory. This study generalizes the previous derivations obtained for multi-component isotropic media. The theory presented is applied to radiatively characterize an example two-component anisotropic medium that finds application in solar energy conversion. Its directional, continuum-scale radiative properties are calculated by incorporating the exact morphology obtained by computed tomography. The continuum-scale properties are compared to those predicted assuming an isotropic medium.