A generalized interface model for joints and cracks in quasi-brittle materials is formulated. The proposed model marries an existing fracture mechanics based one developed for monotonic loading of concrete with another frictional based model developed for the cyclic response of rock joints to address the (reverse) cyclic response of rough surfaces in the presence of cohesive stresses. The properties of the model and its capability to capture several experimentally observed behaviors are shown by the numerical simulations performed. This joint constitutive model is particularly suitable to simulate the seismic response of dam/rock joints subjected to seismic excitation, or of concrete joints under reverse cyclic loading.