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Bioinspired nacre-like composites have attracted increasing research interests recently. They are typical composites with brick-and-mortar structure and usually employ a combination of hard material and soft material to achieve a good balance between stiffness and toughness. Impact response analysis of such composites is difficult due to their complex structure and interface. In this work, an effective finite element method-smoothed particle hydrodynamics (FEM-SPH) coupling approach is developed for impact response analysis of composite plates with brick-and-mortar structure. In the approach, hard material taking up the bulk of the composite plate is modeled with the SPH method, and soft material forming thin layer structures in the composite plate is modeled with FEM. A coupling algorithm considering failure behavior is proposed to model bonding interfaces between FEM parts and SPH parts. A particle-to-particle SPH contact algorithm is employed to handle contacts between SPH parts, and a penalty-based FEM-SPH contact algorithm is implemented to treat contacts between FEM parts and SPH parts. The developed coupling approach is used to calculate stress wave propagation in two bonded plates of the same material and different materials and a composite plate with brick-and-mortar structure. The accuracy of the coupling approach is validated by comparing the calculated results with those of analytical method and FEM. The coupling approach is then used to simulate the effects of some factors on the impact damage of composite plates with brick-and-mortar structure. The coupling approach can conveniently model the complex structure and bonding interface of the composite plates and is capable of capturing interface failure and fragmentation of the major composition of the composite plates during impact events. It provides a promising alternative for the impact response analysis of brick-and-mortar composite structures.