We examine transport of holes in asymmetric triple-barrier p-Si/Si 0.8 Ge 0.2 resonant tunneling structures with different middle barrier widths ͑Lϭ10, 20, and 30 Å͒ for Tр4.2 K. The two-dimensional ͑2D͒ heavy-hole ͑HH͒ and light-hole ͑LH͒ subbands in each of the two quantum wells interact through interwell tunneling, resulting in 2D double-well subbands. We identify resonances corresponding to tunneling transitions through these double-well subbands using a simple wave-function formalism. The observed resonances correspond to strong HH-HH coupling with the addition of weaker HH-LH coupling for the narrowest middle barrier width, Lϭ10 Å. We also present measurements displaying the HH-LH interaction strength dependence on high magnetic fields parallel to the current, B ʈ. The weak HH-LH interaction quenches as B ʈ approaches 10 T.