We investigate the angular dependence of the reflectance from an isotropic medium consisting of optically large and anisotropic, randomly oriented domains, assuming a highly refractive, isotropic, and homogeneous incidence medium, which is presumed to have a higher refractive index than any of the domains' principal indices of refraction. By employing average reflectance and transmittance theory, we are able to show that the onset of total reflection is considerably shifted to higher angles of incidence compared with an isotropic medium with domains that are small compared with the wavelength. The onset of total reflection for a random medium with large domains is found to be dependent only on the largest principal index of refraction of the domains, assuming that all domains have the same optical properties. Therefore the shift of the onset depends on the magnitude of the optical anisotropy of the domains. Even in the case of a small optical anisotropy, large cross-polarization terms are predicted in the vicinity of the onset of total reflection. These terms show a pronounced maximum near that onset and extend beyond it.