The interfacial fracture of rock joints is an important although easily ignored issue in jointed rock engineering. To conduct this study, an interface crack model of rock joints was proposed. By analyzing the ratio of stress intensity factor to fracture toughness, the fracture mode of the interface crack was studied. Based on the Mohr-Coulomb criterion, an interface fracture criterion considering T-stress was established. To verify the proposed fracture criterion, laboratory and numerical tests were conducted. Finally, the effect of relative critical size α, internal friction angle φ and cohesion c on the initiation of an interface crack was comprehensively discussed. It is concluded that the proposed fracture criterion can predit the initiation of the interface cracks properly. With an increase in cohesion c, mode II fracture toughness KII also clearly increases. When the absolute value of KI is small, the effect of α is much larger than that of φ. In addition, with an increase in the absolute value of the mode I stress intensity factor, the φ of the joint plays a more important role in the initiation of the interface crack.