As an extension of previous work which was based on the isotropic interaction approximation, absorption spectra in the rotational and fundamental bands of H-2, induced by collisions with He, are calculated by numerical integration of the close-coupled Schrodinger equation to account for the anisotropy of the interaction potential. A refined quantum chemical dipole surface of interacting H-2-He pairs is also obtained with an extended grid of molecular geometries. This dipole surface agrees generally well with previous results, but is smaller by about 5% in the isotropic overlap term which is significant only in the fundamental band. The effects of the anisotropy of the interaction are to reduce the peak intensities of the Q and S lines by roughly 10% and to increase absorption in the far wings by a similar amount. The accuracy of the dipole surface as well as that of the ab initio interaction potential that enters the calculations of the spectra are believed to permit the prediction of absolute spectral intensities with an accuracy of about +/- 5%. Comparisons with the available measurements show very good agreement of the shapes of the spectral profiles, but the absolute intensities differ by up to 10% in some cases. These remaining differences between theory and measurements appear to be random and are generally smaller than the differences among comparable measurements. Our results should therefore provide a reliable basis for predicting absorption by H-2-He pairs for temperatures and frequencies for which no laboratory measurements exist. This fact is of a special interest, for example, for the spectroscopic analyses of the atmospheres of the outer planets.