The rovibrational energy-level structures of BaH$^+$ and BaD$^+$ in their X$^+$~$^1\Sigma^+$ electronic ground state have been characterised by pulsed-field-ionisation zero-kinetic-energy photoelectron spectroscopy following resonance-enhanced ($1+1^\prime$) two-photon excitation from the BaH/BaD...