We extend our models of the vertical structure and emergent radiation field of accretion disks around supermassive black holes described in previous papers of this series. Our models now include both a self-consistent treatment of Compton scattering and the effects of continuum opacities of the most important metal species (C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni). With these new effects incorporated, we compute the predicted spectrum from black holes accreting at nearly the Eddington luminosity (L/L-Edd approximate to 0.3) and central masses of 10(6), 10(7), and 10(8) M-circle dot. We also consider two values of the Shakura-Sunyaev alpha parameter, 0.1 and 0.01, but in contrast to our previous papers, we consider a kinematic viscosity that is independent of depth. Although it has little effect when M >10(8) M-circle dot, Comptonization grows in importance as the central mass decreases and the central temperature rises. It generally produces an increase in temperature with height in the uppermost layers of hot atmospheres. Compared to models with coherent electron scattering, Comptonized models have enhanced extreme ultraviolet/soft X-ray emission, but they also have a more sharply declining spectrum at very high frequencies. Comptonization also smears the hydrogen and the He II Lyman edges. The effects of metals on the overall spectral energy distribution are smaller than the effects of Comptonization for these parameters. Compared to pure hydrogen-helium models, models with metal-continuum opacities have reduced flux in the high-frequency tail, except at the highest frequencies, where the flux is very low. Metal photoionization edges are not present in the overall disk-integrated model spectra. The viscosity parameter alpha has a more dramatic effect on the emergent spectrum than do metal-continuum opacities. As alpha increases (and therefore the disk column density decreases), the flux at both the high- and low-frequency extremes of the spectrum increases, while the flux near the peak decreases. Multitemperature blackbodies are a very poor approximation to accretion disk spectra in the soft X-ray region, and such crude modeling may greatly overestimate the accretion luminosity required to explain observed soft X-ray excesses in active galactic nuclei. In addition to our new grid of models, we also present a simple analytic prescription for the vertical temperature structure of the disk in the presence of Comptonization, and show under what conditions a hot outer layer (a corona) is formed.
