We study superconductivity in a two-band model that generalizes the model introduced by Suhl, Matthias, and Walker: All possible interaction terms coupling both bands are included. The pairing interaction is assumed to originate in the momentum dependence of the intraband interactions that arises in the model of hole superconductivity. The model generically displays a single critical temperature and two gaps, with the larger gap associated with the band with strongest holelike character to the carriers. The dependence of the critical temperature and of the magnitudes of the gaps on the various parameters in the Hamiltonian is studied.