A general formulation is presented to model photodissociation processes in which internal conversion is followed by unimolecular dissociation over an exit barrier; this classification of dissociation mechanism results in a nonstatistical product state distribution. The energy available to products is divided into independent statistical and impulsive energy reservoirs. The statistical reservoir considers direct projections of a vibrational microcanonical ensemble at the transition state (TS) onto product quantum states, conserving vibrational adiabaticity and angular momentum. The impulsive reservoir represents the energy released in passing from the TS to products; this reservoir is treated assuming sudden dissociation of the zero-point TS wave function using a combination of Franck-Condon and impulsive models. We derive the statistical adiabatic impulsive model, which convolutes these two energy reservoirs, to predict the product translational energy distribution for nonstatistical dissociation over a barrier. Two test cases are modeled and compared with experimental data: unimolecular dissociation of acetyl radicals and photodissociation of vinoxy radicals via the (B) over tilde(2)A "-(X) over tilde(2)A " (2)A " band.