Hydrogen-electricity integrated multi-energy systems are promising approaches to reduce carbon emissions in ports. However, the stochastic nature of renewable energy and the imbalance between the renewable generation and load demand in ports necessitate the design of an appropriate coupled hydrogen-electricity energy storage systems (CHEESS). This paper proposes a multi-objective optimization model for CHEESS configuration in random imbalanced port integrated multi-energy systems (PIMES), aiming to minimize its life-cycle cost and carbon emissions through co-optimization of sizing and energy management. A hierarchical two-stage framework is proposed to solve the multi-objective model. The proposed optimization framework is applied to a real PIMES at the Ningbo-Zhoushan Port. The results show that the proposed method can save 10.54 % of the monetary cost and 19.67 % of carbon emissions over the entire life-cycle of the system. The study demonstrates that the proposed framework has the potential to generate significant economic and environmental benefits and provides a feasible solution for port authorities seeking to implement CHEESS, aiming to promote sustainability in port operations.