Experimental tests were conducted on the composite rock-concrete specimens with granite, sandstone, and C30/C50 concrete to study the interfacial fracture process under three-point bending and four-point shear conditions. A unified interfacial crack initiation criterion expressed by the stress intensity factors (SIFs) was fitted by the SIFs corresponding to the interfacial crack initiation based on the experimental data. By combining with the fictitious crack model, the crack initiation criterion can be transformed into the crack propagation criterion by considering the contributions of the cohesive forces in the fracture process zone. By assessing the relationships of the interfacial propagation criterion and the maximum circumferential stress criteria of the rock and concrete, the potential interfacial crack propagation paths can be predicted. Furthermore, numerical analyses were carried out by introducing these criteria to simulate the complete fracture process of the rock-concrete interface, where the predicted P-CMOD curves and crack trajectories showed good agreements with the experimental data. Finally, by taking a classic gravity dam in practical engineering as an example, the effects of the water levels, initial crack length and crack propagation length on the fracture behaviour of concrete, rock and their interface were investigated. The whole fracture processes for various fracture parameters of the rocks, concretes and their interfaces were simulated numerically. The results indicated that the employed method was effective for the safety assessment of the gravity dam and the application of these propagation criteria is convenient because only the initial fracture toughnesses of the rocks, concretes and their interfaces are required.