Coherent tunneling between two InAs quantum dots forms delocalized molecular states. Using magnetophotoluminescence spectroscopy we show that when holes tunnel through a thin barrier, the lowest energy molecular state has bonding orbital character. However, as the thickness of the barrier increases, the molecular ground state changes character from a bonding orbital to an antibonding orbital, confirming recent theoretical predictions. We explain how the spin-orbit interaction causes this counterintuitive reversal by using a four-band k . p model and atomistic calculations that account for strain. ; peer reviewed: yes ; NRC Pub: yes