The photodissociation dynamics of surface-adsorbed HCl+ is studied using both time-dependent and time-independent quantum mechanical methods. The photodissociation line shapes and photofragment angular distributions are calculated following excitation to the (2)(2) Sigma and the (2)(2) Pi electronic states, correlating with Cl+ + H and with Cl + H+, respectively. Complementary insight is gained by analyzing also the classical photodissociation dynamics. We find pronounced shifts and modifications of the photodissociation line shapes, which depend sensitively on the fragmentation channel and reflect surface-induced modification of the adsorbed state and the excited HCl+ potential energy surfaces. The quantum mechanical angular distributions exhibit a rich, energy-dependent structure, which differs substantially for the two fragmentation channels. Assisted by the classical trajectory results, we ascribe the structure to surface-induced rainbow scattering. The sensitivity of the photodissociation line shape and the angular distribution to the initial orientation of the adsorbate and to details of the substrate-adsorbate interaction in the excited manifold is illustrated.