We have measured the unenhanced, nonresonant surface Raman spectra of one monolayer of hydrogen bound to flat and stepped Si(111) surfaces prepared using a novel, aqueous fluorine etch. The orientation and normal mode composition of adsorbate vibrations are obtained from polarized, angle-resolved Raman spectra using a 3-layer dielectric model. This approach requires the experimental determination of both the anisotropy in the dynamic polarizability of the adsorbate bond and the effective dielectric constant in the vicinity of the adsorbate. The measured Si-II bond anisotropy is 0.263+/-0.028 in good agreement with gas phase measurements. The adsorbate dielectric constant is measured to be 3.78+/-0.20; this response is clearly nonlocal and predominantly due to polarization of the underlying silicon lattice. Using this technique, we find that the step dihydride on a Si[6(111)-($($) over bar$$ 1 $($) over bar$$ 12)] surface is rotated 37 degrees+/-4 degrees from the surface normal in good agreement with the 31 degrees predicted by ab initio cluster techniques, but significantly larger than the 12.5 degrees predicted by pseudopotential slab calculations. In contrast to both theoretical predictions, the normal modes of this step dihydride display little concerted motion indicating that subsurface relaxation near the step edge reduces steric interactions much further than predicted. The observed anisotropic etch rates, evidenced by the production of atomically straight steps, are explained in terms of the measured distortion at the step edge.