(Abridged) The propagation of ionizing radiation through model atmospheres of terrestrial-like exoplanets is studied for a large range of column densities and incident photon energies using a Monte Carlo code we have developed to treat Compton scattering and photoabsorption. Incident spectra from parent star flares, supernovae, and gamma-ray bursts are modeled and compared to energetic particles in importance. We find that terrestrial-like exoplanets with atmospheres thinner than about 100 g cm^-2 transmit and reprocess a significant fraction of incident gamma-rays, producing a characteristic, flat surficial spectrum. Thick atmospheres (>~ 100 g cm^-2) efficiently block even gamma-rays, but nearly all incident energy is redistributed into diffuse UV and visible aurora-like emission, increasing the effective atmospheric transmission by many orders of magnitude. Depending on the presence of molecular UV absorbers and atmospheric thickness, up to 10% of the incident energy can reach the surface as UV reemission. For the Earth, between 2 x 10^-3 and 4 x 10^-2 of the incident flux reaches the ground in the biologically effective 200--320 nm range, depending on O_2/O_3 shielding. Finally, we suggest that transient atmospheric ionization layers can be frequently created at low altitudes. We conclude that these events can produce frequent fluctuations in atmospheric ionization levels and surficial UV fluxes on terrestrial-like planets.
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