A FEM-SPH coupling approach is developed for the dynamic response analysis of composite plates with brick-and-mortar structure. An effective coupling algorithm considering failure behaviour is proposed to model bond interfaces between FEM parts and SPH parts. Penalty-based FEM-SPH contact algorithm and FEM contact algorithm are implemented to treat contacts between FEM parts and SPH parts and self-contacts of FE parts. The accuracy of the proposed coupling algorithm is examined by the calculation of stress wave propagation in two bonded plates of the same material and different materials. The FEM-SPH coupling approach is firstly employed to analyze the low-velocity impact response of a composite plate with brick-and-mortar structure, which is composed of a hard brittle material and a soft ductile material. The effectiveness of the coupling approach is validated by comparing the analysis results with those of FEM. The FEM-SPH coupling approach is then applied to investigate the response of brick-and-mortar composites of different structural parameters subjected to impacts of different velocities.