Integrated energy systems are an effective path to achieve the "dual carbon" goals. In order to improve the multi-energy complementation and low-carbon characteristics of the integrated energy system, an optimal scheduling model of the integrated energy system was proposed, which took into account the joint operation of carbon capture power plant, waste incineration power plant, electricity-to-gas and flexible dual-response of supply and demand. On the demand side, the transfer of electricity and heat loads in time and between different types were considered. For the uncertainty of renewable energy sources, Latin hypercube sampling was used to generate stochastic scenarios and Kantorovich was used to cut down the scenarios. Finally, the optimal scheduling model of the supply-demand flexible response integrated energy system was established with the goal of minimizing the total operating cost by taking into consideration of the system's low-carbon nature and economic performance. The results show that the proposed model can effectively improve the green energy consumption capacity, further reduce the carbon emission of the integrated energy system and minimize the economic operation cost.