A new method is suggested for determining the molecular orientation in adsorbed films with uniaxial and biaxial anisotropy from two (s- and rho -polarized) IRRAS spectra of the same sample, measured at the optimal angle of incidence. The method is simple, does not use the film thickness, and is internally stable with respect to the uncertainty in the input optical parameters of the anisotropic film. The advantages and limitations of the method are discussed. To validate the method, we determined the orientation of hexadecylamine and hexadecyl alcohol adsorbed on a quartz surface. It is shown that at a concentration above the concentration of 2D precipitation but below the concentration of 3D precipitation, hydrocarbon chains in the adsorbed amine monolayer are well-packed in a monoclinic (biaxial) subcell with a tilt angle of about 30 degrees. Chaotically arranged crystallites of the amine molecules appear at the surface at a concentration higher than the concentration of 3D precipitation. Adsorbed monolayers of the alcohol turn out to have a hexagonal structure, in which the hydrocarbon tails are "flip-flop" positioned and tilted by 25-30 degrees from the surface normal.