To promote the efficient mobilization of flexibility resources on the user side in integrated energy systems, a dual incentive mechanism integrating economic compensation and carbon offset is constructed, and the research is conducted in combination with a demand response optimization model. Firstly, based on users′ response characteristics to multiple energy sources such as electricity, heat, and gas, flexible loads are categorized into three types of flexibility loads for scheduling, and a joint incentive strategy incorporating economic and carbon compensation is introduced. Secondly, a bi-level game model between integrated energy operators and load aggregators is established, combining multi-dimensional demand response constraints and Stackelberg game theory to solve for optimal benefit allocation. Additionally, to enhance the optimization capability of the algorithm, an adaptive multi-mutation differential evolution algorithm is proposed. Finally, simulations under different scenarios demonstrate that the model significantly reduces system operational costs and carbon emissions while also prove that the proposed algorithm exhibits superior optimization capability.