The utilization of combined heat and power (CHP) units is a key way to enhance renewable energy accommodation. However, carbon emissions of CHP challenge the pollution and economic optimization of integrated energy system (IES). To tackle this challenge, we propose a novel model and optimal dispatch for CHP with power-to-gas (P2G) and carbon capture system (CCS), which solves the problems of the carbon source required for P2G and the CHP's carbon emissions by the optimal dispatch in IES. The model takes the CHP, P2G, and CCS as a whole system. The operation rule of the model is developed, and its coupling characteristics of electric power, heat power, gas power and carbon are analyzed. Correspondingly, the optimization strategy of IES considers the proposed model and carbon trading mechanism. The optimal dispatch model of IES is established and solved by YALMIP, and GUROBI. Our method is verified by simulation. Compared with other conventional models, the accommodation capacity of renewable energy with the proposed method is enhanced, and the carbon emissions and operating costs of IES are also reduced.