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With the increasing number of integrated energy system (IES) construction, a multi-agent system group composed of multiple IESs would be formed in a certain region. Moreover, complex uncertainties gradually existed in the IES which affect the system optimal situation and optimization results. In order to take full use of each agent's advantages and improve the performance of the whole region under uncertainty, this paper focuses on the multiple energy types' interaction of multi-agent IESs within the region to realize the stable operation, economic and environmental improvement of each agent and the whole region. To this aim, a multi-objective multiple energy types' multi-agent interactive optimization model considering energy demand and renewable energy output uncertainties was built. The model was based on Nash bargaining cooperative game theory and took economy, flexibility and carbon emission as objectives. Moreover, energy interaction scheduling and its corresponding price can be optimized through the model. The results of non-cooperative operation mode without interaction and cooperative operation mode with interaction were compared to analyze the superiority of interaction from the cost, carbon emission and flexibility aspects. The overall regional carbon emission and the economic cost has been reduced by 13.84% and 9.94%, for each IES, the carbon emission and economic cost could reduce by up to 41.5% and 44.5%. Moreover, the flexibility of the IES was correspondingly increased by nearly 47%. These results denoted that after multi-agent interaction, not only the overall region's energy, economic and environmental performance are improved, but also that of each agent are significantly improved. In addition, different energy types among multiple agents could be effectively used and regional joint energy storage is realized, improving the region flexibility level and resilience. • A multi-objective integrated energy systems interaction model is established. • The interaction model considers multiple energy types and uncertainties. • The model can improve economy and flexibility of each system agent and the region. [ABSTRACT FROM AUTHOR]