Using recent X-ray and gamma-ray observations of terrestrial gamma-ray flashes (TGFs) from spacecraft and of natural and rocket-triggered lightning from the ground, along with detailed models of energetic particle transport, we calculate the fluence (integrated flux) of high-energy (million electronvolt) electrons, X rays, and gamma rays likely to be produced inside or near thunderclouds in high electric field regions. We find that the X-ray/gamma-ray fluence predicted for lightning leaders propagating inside thunderclouds agrees well with the fluence calculated for TGFs, suggesting a possible link between these two phenomena. Furthermore, based on reasonable meteorological assumptions about the magnitude and extent of the electric fields, we estimate that the fluence of high-energy runaway electrons can reach biologically significant levels at aircraft altitudes. If an aircraft happened to be in or near the high-field region when either a lightning discharge or a TGF event is occurring, then the radiation dose received by passengers and crew members inside that aircraft could potentially approach 0.1 Sv (10 rem) in less than 1 ms. Considering that commercial aircraft are struck by lightning, on average, one to two times per year, the risk of such large radiation doses should be investigated further.