With the rapid development of China's distributed energy system, a large number of integrated energies microgrids appear on the energy-use side, and the coordinated operation of adjacent integrated energy microgrids in the form of microgrid clusters will be an important trend for the future development of integrated energy microgrids. This paper proposes a coordinated operation method suitable for integrated energy microgrid clusters. It aims to coordinate the integrated energy microgrids belonging to different stakeholders and seek the optimal operation scheme of the microgrid cluster system under the condition of sharing limited information and making decisions independently. Considering that the integrated microgrid clusters system usually contains lots of renewable energy, in order to improve the robustness of the scheme to deal with the uncertainty of renewable energy output, a chance-constraint programming method is adopted to effectively curb the influence of uncertainty. Finally, by analyzing a microgrid cluster system with electric power and natural gas, the results show that the proposed method can improve the economy and security of the system and realize the tradeoff between the two characteristics. This work is supported by the the National Natural Science Foundation of China (No. U2066214) and the Project of State Grid Shanghai Electric Power Company (No. SGSHDK00DYJS 1900179).