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.