We describe the valence-band holes of quantum dot molecules formed by two vertically coupled disks, using a four-band k . p Hamiltonian. It is shown that the strong spin-orbit coupling of the valence band introduces characteristic features in the hole tunneling, which are not captured by the usual single-band heavy-hole approximation. Therefore, a treatment of hole states as multiband Luttinger spinors is required. Within this description the parity symmetry in the vertical direction is lost, and chirality symmetry must be used instead. Effects of spin-orbit coupling on the hole and exciton states, as well as on the optical transitions are discussed. We show that, with increasing interdot distance, the spin-orbit interaction leads to a bonding-antibonding ground-state transition and to quenching of the excitonic emission. These results are relevant to recent experiments.