A single band belonging to the A∼′2Δ-X∼2Σ+ band system has been rotationally analyzed for each of the two isotopologues, BaOH and BaOD, using high-resolution V-type optical–optical double resonance spectroscopy. BaOH and BaOD molecules were synthesized in a Broida-type oven. High-resolution spectra were recorded by monitoring the dip in fluorescence of the B∼2Σ+-X∼2Σ+ transition excited by a single-mode ring dye laser (pump laser), whilst a single-mode Ti:Sapphire laser scanned the corresponding A∼′2Δ-X∼2Σ+ transition. The observed spectra resemble a typical 2Π-2Σ transition, believed to emanate from single or triple quanta of the bending vibration in the A∼′2Δ state. Measured rotational lines have been assigned and rotational and fine structure parameters determined through a combined least-squares fit with the millimeter-wave pure rotational data of the X∼2Σ+ state. Previous analyses of the A∼2Π-X∼2Σ+ transitions of BaOH and BaOD yielded significantly different spin–orbit coupling constants, which were attributed to possible global and local perturbations arising from vibrationally-excited bands of the A∼′2Δ state. Although the newly observed A∼′2Δ state bands have not been conclusively assigned a specific spin state, the derived Ω-doubling constants show significant 2Π1/2 character, further indicating strong interactions between the A∼2Π and A∼′2Δ states of BaOH. To validate these conclusions, ab initio calculations have been carried out to further understand the nature of the BaOH excited states. The D∼′2Σ+, D∼2Σ+, C∼2Π, B∼2Σ+, A∼2Π, A∼′2Δ and X∼2Σ+ states have been characterized by means of multireference configuration interaction calculations using the MOLPRO software. Calculated vertical term energies show relatively good agreement with existing optical data.