Tunneling of holes through single-barrier structures is theoretically studied. Due to the multi-band nature of the valence band edge, it is necessary to take into account several paths of tunneling between bands with different effective masses. Calculated tunneling coefficients for GaAs/AlAs/GaAs and Si/GaAs/Si structures demonstrate that the interband tunneling is large enough to affect the tunneling current. The tunneling current is also affected by the phase difference between amplitudes through different paths when in-channel states are coherent. The effect of such interference is discussed.