In the context of global industrialization, integrated energy systems (IES) have emerged as a crucial means of facilitating green and low-carbon transformation. To comprehensively explore the potential for carbon reduction through source-load synergy and achieve low-carbon and high-efficiency operation of the system, an IES optimal scheduling method that incorporates a reward and punishment mechanism for dynamic electricity and thermal carbon emission factors is proposed. Firstly, the concepts of energy coupling and thermal energy cascade utilization are considered, and an IES-coupled equipment cascade utilization model with carbon capture is established with the objective of realizing high-grade use of thermal energy in combination with thermal load demand. Secondly, an improved IES dynamic electricity and thermal carbon emission factors model is proposed to characterize the carbon emission intensity and renewable energy consumption capacity. Based on this, an integrated demand response (IDR) mechanism driven by electricity, thermal reward, and carbon price is established to guide users toward low-carbon behaviors and renewable energy consumption. Finally, a two-stage optimal scheduling model is constructed. In the pre-scheduling phase, the initial scheduling plan is solved, and the load distribution is adjusted by the integrated demand response. In the re-scheduling phase, the load curve is updated to obtain the final scheduling plan. Through simulation verification, the proposed scheduling model reduces carbon emissions by 7.7 %, improves the renewable energy consumption rate by 4 %, and reduces the comprehensive operating cost of the system by 4.3 %, which indicates that the method proposed in this paper can effectively promote the emission reduction and consumption and reduce the operating cost of the system.