In order to solve the problems of low energy cascade utilization degree, insufficient analysis of response characteristics of equipment differentiation, and prominent low-carbon demand in the integrated energy system, this paper researches the optimization scheduling of heat pump energy storage coupling systems considering carbon certification synergy and response characteristics. Firstly, a system operation framework and mathematical model were constructed using the heat pump energy storage coupling system as the research object. Secondly, a carbon certification collaborative mechanism was designed, and the uncertainties in the coupled system were decomposed based on the CEEMDAN-IIR method to match the response characteristics of the equipment. Thirdly, a coupled system operation optimization model was constructed to minimize the total system cost and maximize new energy consumption. Finally, an empirical analysis was conducted to verify the model’s effectiveness using a certain coupled system as an example. The results of the example show that: 1) The heat pump energy storage coupling system can reduce operating costs by 22.5% compared to other systems; 2) Compared with the carbon certificate collaborative mechanism, a single carbon trading mechanism increases carbon dioxide emissions by 20.48 kg and reduces the new energy consumption rate by 1.32%; 3) Compared with the EMD algorithm and EEMD algorithm, the CEEMDAN-IIR method can more effectively suppress false modes, and improve the stability and accuracy of decomposition.