The hybrid energy storage system (HESS) comprising batteries and supercapacitors has garnered extensive application and research attention in microgrids due to its synergistic integration of complementary advantages. Prevailing research on HESS control strategies predominantly focuses on DC bus voltage regulation and power distribution, while often neglecting potential enhancements in battery cycle lifespan and overlooking the proactive advantages of energy storage systems in microgrid energy dispatch participation. In this context, this paper proposes a multi-objective coordinated control strategy for HESS based on battery grouping in microgrids. The proposed methodology implements two battery groups with time-shifted alternating charging/discharging operations, thereby establishing a coordinated control framework that simultaneously addresses four critical objectives: (1) DC bus voltage stabilization, (2) optimized power distribution between heterogeneous storage units, (3) supercapacitor state-of-charge (SOC) equilibrium maintenance, and (4) precise tracking of dispatch power commands. Comprehensive verification through long-term simulation scenarios demonstrates the strategy's efficacy. The results demonstrate that the multi-objective coordinated control strategy for hybrid energy storage can enhance the self-balancing effect of supercapacitor SOC, improve the conformity of battery scheduling power, and extend the lifespan of batteries.