The article highlights the importance of integrated energy systems in the future energy transition, emphasizing the need for multi-energy supply modes to optimize energy utilization and reduce carbon emissions. It introduces a cooperative game framework for electricity-heat-hydrogen multi-energy sharing among integrated energy systems, aiming to enhance regional efficiency. By applying the generalized Nash bargaining theory and the adaptive alternating direction method of multipliers algorithm, the model addresses alliance benefit maximization and benefit distribution equilibrium. Case analysis shows a significant reduction in operational costs and carbon emissions, validating the model's computational superiority. The study emphasizes the positive impact of collaborative optimization on economic operation and green low-carbon transition in regional energy systems, promoting efficient energy utilization and resource allocation.