Delamination is a critical mode of failure that occurs between plies in a composite laminate. The cohesive element, developed based on the cohesive zone model, is widely used for modelling delamination. However, standard cohesive elements suffer from a well-known limit on the mesh density—the element size must be much smaller than the cohesive zone size. This work extends the line of research on structural cohesive elements onto 3D mixed-mode problems. A new triangular Kirchhoff–Love shell element is developed for orthotropic materials to model the plies. A new structural cohesive element, conforming to the shell elements of the plies, is developed to model the interface delamination. The proposed method is verified and validated on the classical benchmark problems of Mode I, Mode II, and mixed-mode delamination of unidirectional laminates, a recent unidirectional benchmark problem with curved delamination front, as well as the single-leg bending problem of a multi-directional laminate, significantly increasing the range and complexity of applicable problems as compared to the previous works. All the results show that the element size in the proposed models can be ten times larger than that in the standard cohesive element models, with more than 90% reduction in CPU time, while retaining prediction accuracy. This would then allow more effective and efficient modelling of delamination in composites without worrying about the cohesive zone limit on the mesh density.