In a hybrid AC/DC multi-microgrid system, the economy and operational reliability are affected by the configuration of capacity. Considering the advantages of hybrid energy storage systems based on electric and hydrogen energy storage (electrolyzer/fuel cell/hydrogen storage tank), this paper establishes an electric-hydrogen hybrid energy storage multi-microgrid system framework. Secondly, for the said system, a multi-microgrid operation control strategy considering the real-time energy supply and demand and energy storage status of the system is proposed to ensure the economic and reliable operation of the system. A power interaction constraint model is introduced into the capacity optimization configuration model, and the proposed operational control strategy is embedded in the configuration process. Finally, an example is used to verify the necessary of power interaction constraints, and the gray wolf-sine cosine optimization algorithm is used to solve the configuration model. The results obtained are better than those of Grey Wolf optimizer and mutation particle swarm optimization algorithm. Through the simulation of annual operating conditions, the effectiveness of the optimization strategy proposed and the advantages of the electric-hydrogen hybrid energy storage system in seasonal energy storage are verified. This work is supported by the National Natural Science Foundation of China (No. 51977181).