Biological staggered composites, like bone, nacre, and dentin, possess the superior capacity of energy dissipation than that of conventional materials. In these nanocomposites, different staggered microstructures are widely observed, for example, symmetric staggered structures with regular platelet layouts and asymmetric staggered structures with offset and stairwise platelet layouts. In addition, the thickness of platelets in these biological materials is at the nanoscale, and the distance between the adjacent ends of platelets is large enough in staggered structures, which indicates the interface effect and tension region cannot be ignored in staggered nanocomposites. In order to investigate the possible synergistic effect of the platelet layouts, interface effects, and tension region on the dynamic properties of the nanocomposites, a generalized tension-shear chain model (TSCM) with tension region (TR) is proposed. According to the analytical solutions derived, the staggered nanocomposites with optimal structures can be designed to obtain superior energy dissipation capacity. Considering different loading frequencies in natural environment, the optimal dynamic properties of nacre can be achieved with a regular staggering platelet distribution, while the optimal dynamic properties of bone can be achieved when the number of periodic stairwise staggering platelets is appropriately smaller. These optimal platelet layouts in nacre and bone are consistent with the experimental results reported in many literatures. Therefore, the energy dissipation capacity of staggered nanocomposites can be highly improved, based on the profound understanding of the damping mechanism in biological nanocomposites.