A quantum mechanical theory is described for diatomic photodissociation processes to atomic fine structure states for which more than one atomic term limit must be explicitly considered. The theory is employed to treat the photodissociation of OH molecule. Two frame transformation matrices are constructed and incorporated, for the first time, to describe the correlations between two oxygen terms [O(P-3) and O(D-1)] and the adiabatic Born-Oppenheimer states. We find that very interesting dynamics results from the quantum interferences between electronic states. Near the dissociation threshold to O(3P), asymptotic interactions between asymptotically degenerate states correlating to O(P-3) term are shown to manifest as multichannel resonances. At energies between thresholds to O(P-3) and O(D-1) terms, quantum interferences between A (2) Sigma(+) and (2) Sigma(-) states are predicted to result in asymmetric resonances. Partial cross sections to the triplet oxygen fine structure states O(P-3(j), j = 0,1,2) exhibit different degrees of asymmetry due to the combined effects of the quantum interference between A (2) Sigma(+) and (2) Sigma(-) states crossing in the Franck-Condon region, and the asymptotic interactions among (4) Sigma(-), (2) Sigma(-), and (4) Pi states correlating to O(P-3). Consequently, the branching ratios of O(P-3(j), j = 0,1,2) exhibit strong variations across the asymmetric resonances, suggesting the possibility of controlling the product distributions by tuning at the excitation wavelengths across a single asymmetric resonance in one-photon process. Interference between the dissociative (2) Delta and 2 (2) Pi states, correlating with O(D-1) term, are shown to give rise to highly oscillatory variations of the dissociation cross sections to O(D-1) at energies above the threshold to O(D-1).