We have observed resonant tunneling of holes through double-barrier AlAs-GaAs-AlAs structures sandwiched between p+-GaAs regions. The resonances appeared as negative resistance regions in the current-voltage characteristics perpendicular to the interface planes. A set of resonant structures was already visible at high temperatures (T≅250 K) while an additional set was observable only at low temperatures (T≤100 K). Although in principle the sets can be attributed to tunneling of light and heavy holes, respectively, an analysis of the number and relative voltage position of the resonances suggests that considerable band mixing occurs. The application of a strong magnetic field, parallel to the tunneling current, introduced shifts in the resonances which support that interpretation.