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With the continuous increase of electrification in seaports, the single energy supply mode of seaport microgrid is evolving towards multi-energy integration. Aimed to achieve the goals of peak carbon and carbon neutrality, an optimal carbon trading mechanism-based allocation scheme of hybrid electric and thermal storage system is proposed to further maximize the economic and environmental benefits. First, the integrated energy system model of a seaport is established, incorporating a scheme within the carbon trading market. Then, a bi-level optimization framework is proposed, in which the upper layer is utilized to optimize the allocation of the hybrid energy storage system and the lower layer is employed to optimize the operation. Afterwards, a combination algorithm of the mesh adaptive direct search and the adaptive chaotic particle swarm optimization is developed to solve the proposed problem. Finally, the real-world data of Tianjing port is utilized to verify the method. The numerical results demonstrate that with the help of the proposed method, both the cost and carbon emissions are dramatically reduced.