Cooperative interconnection of multi-energy microgrids can enhance the flexibility and reliability of energy supply. Aiming at the problems of multi-energy complementarity and benefit distribution in the cooperative operation of multi-energy microgrid clusters, an interactive cooperative operation strategy based on a stable grand coalition is proposed. First, equipment models of an individual multi-energy microgrid and an electricity-heat demand response model based on utility cost are established. Next, an interactive cooperative operation model for multi-energy microgrid clusters based on cooperative game theory is formulated, and it is proven that the proposed model satisfies superadditivity and balancedness. These properties indicate that interconnected multi-energy microgrids will form a stable grand coalition to coordinate multi-energy complementary behavior. Then, a nucleolus-based benefit allocation scheme is adopted to distribute the total benefits generated by cooperation ex-post. Finally, a nested primal-dual algorithm is designed to accurately solve the nucleolus. Compared with conventional exact nucleolus solution algorithms, the proposed method reduce the number of iterations from 2N to no more than the number of multi-energy microgrids N. Case study results show that the proposed strategy effectively promotes complementary energy utilization among microgrids and improves the benefit level of individual microgrids. The nucleolus-based allocation scheme is fair and reasonable, and the nested primal-dual algorithm significantly reduces the computation complexity of nucleolus-based allocation.