As part of the "dual carbon" objectives, using excess clean energy to electrolyze water and produce hydrogen is crucial to achieving zero carbon emissions in the energy and power industries. The markets for hydrogen, carbon, and green certificates display significant interconnections. This study suggests a coordinated optimization model for integrated energy systems under multi-market coupling to facilitate the deep integration of hydrogen and carbon. Firstly, investigate the interactive relationship between hydrogen trading, CCER trading, green power certificate trading, and carbon trading mechanism, which will contribute to accurately quantifying the dispatch costs of each unit under the guidance of the coupled market mechanism. Secondly, a game optimization model for integrated energy systems is created, with hydrogen sales operators as leaders and hydrogen sales companies and customers as followers. Finally, the enhanced Kriging meta-model is employed to precisely simulate the price response patterns of hydrogen trading operators and resolve the master-slave game model. The results of the case study analysis show that the model can deeply integrate hydrogen, carbon, and green certificate markets via carbon and hydrogen prices. This integration can lead to improved economic and low-carbon functioning of integrated energy systems.