The interface crack is the typical defect in fracture mechanics, and it often exists inside the layered composite rocks (LCRs). How does it respond to the stress circumstances with a large anisotropy? Is of paramount importance in the stability evaluation of underground engineering. This issue is addressed in this study where the true triaxial tests with the loading rate of 0.05 mm/min are conducted on the two-layered sandstone-granite composite structures containing the interface cracks. Sandstone and granite have a strength of 92.1 and 135.4 MPa, respectively. Results show that the interface crack significantly weakens the LCR strength under true triaxial stress. The interface crack tips, as typical stress concentrator, are revealed as the main sources of fracture initiation and propagation, and the interface crack tips are also found as an essential joint for the fracture containment within the weaker layer. The fracture cluster is formed ahead of the interface crack tip where tensile fracture co-exists with shear fracture. Moreover, the macro-failure initiation mode exhibits the interface crack tip fracture in the quasi-3D failure manner. Main failure planes of LCRs appear sub-orthogonally to σ3 and display the mode of σ3-transverse-symmetric fracturing. Finally, the coupling mechanisms among the interface crack, the stress anisotropy and the mechanical contrast between the layers are revealed.