It is shown analytically and experimentally that, when significant densities of positive and/or negative charge are trapped in the bulk of the oxide, standard thermally stimulated current (TSC) measurements at negative gate bias may not provide accurate estimates of MOS oxide-trap charge densities. Combining TSC measurements at negative bias with capacitance-voltage (C-V) measurements allows useful, self-consistent estimates of trapped electron densities in the oxide to be obtained. However, unless one can determine whether most of the trapped electrons lie in the bulk of the oxide or in border traps, unambiguous estimates of trapped positive charge densities cannot be obtained with negative or positive bias TSC, with or without C-V measurements. Implications are discussed for charge trapping in radiation-hardened thermal oxides, SIMOX buried oxides, and bipolar base oxides.