An extension of the theory for charge emission from monoenergetic grain boundary interface states by thermal emission (TE) and thermionic-field emission (TFE) is presented for states distributed in energy, whose density is either constant or slowly varying with energy as compared to the Fermi function. The importance of TFE increases with the doping concentration

, and the voltage applied across the grain boundary

, and decreases with increasing temperature. Interpretation of the interface state density according to the Seager-Pike-Ginley treatment, which neglects thermionic-field emission, is shown to overestimate the density and underestimate the interface state energies relative to the majority-carrier band.