We calculate the spectrum of X-ray radiation reflected and reprocessed by a partly ionized optically thick medium in an active galactic nucleus. We self-consistently calculate the ionization balance and thermal balance in the medium along with the distribution of X-ray intensity with optical depth. In addition to absorption or scattering of the incident X-rays, we also compute the spectrum of X-rays emitted by the material, including lines, edges, and bremsstrahlung. The albedo of the medium depends primarily on the X-ray ionization parameter (ratio of incident flux to gas density, xi(x)), and secondarily on the UV flux generated by dissipation inside the disk; we locate the critical range of xi(x) over which the albedo increases from small to nearly unity. While the continuum reflection is very weak below 10 keV when xi(x), is small, significant fluxes are emitted in atomic lines and edges in this energy range. In the limit of large xi(x), the albedo below 10 keV increases, but reflection in this band is never ''gray'': some photoelectric absorption remains up to rather large values of xi(x), while at still higher values, inverse Compton scattering amplifies the soft X-ray flux. These features are sufficiently sharp that current and near-future X-ray experiments should permit diagnostic measures of xi(x).