In this study, a general frictional cohesive zone model (FCZM) dedicated to quasi-brittle fracture is proposed to describe the mechanical response of an interface under combined traction or compression and shear loadings. Under combined traction and shear loadings, mixed-mode I + II cohesive zone model, as proposed by Camanho et al. (2003), is used to express the mixed-mode response of the interface and the dependence to the loading path consistent to the one expected in quasi-brittle fracture. Under combined compression and shear loadings, the novelty lies in the proposed coupling between Mode II cohesive behavior and frictional behavior based on the damage level leading to a progressive rising of the frictional stress associated with the softening part of the cohesive behavior of the interface. FCZM thus describes a smooth transition from a cohesive zone to a pure frictional contact zone. Applied to the masonry context, this general FCZM can be fully characterized through two fracture tests carried out on small masonry assemblages. Finally, FCZM is implemented in LMGC90 discrete element code and used to simulate the experimental response of an unilateral cyclic shear test carried out on a triplet of limestone blocks assembled by two mortar joints.