Anisotropic photonic crystal structures consisting of birefringent porous silicon layers with alternating porosity were fabricated. The in-plane birefringence formed as a result of anisotropic etching in Si(110) results in unique multilayered structures with two distinct photonic bandgaps for orthogonal light polarizations. Nonlinear optical studies based on the third-harmonic generation from these structures demonstrate variation in the symmetry of the nonlinear optical response.