The coupled wave theory of Raman and Nath diffraction is extended to the case of thin anisotropic holographic media with grating vector parallel to the medium boundaries. Solutions for the wave amplitudes, diffraction efficiencies, and angular mismatch sensitivities are given in transmission geometries for the case of dielectric modulation. The main difference of the new results with respect to the expressions valid for isotropic media arises due to the walk-off between the wave-front and energy propagation directions. The difference is particularly important in materials with large birefringence, such as organic crystals, ordered polymers, and liquid crystalline cells.