Integrated energy microgrids (IEM) have emerged as an effective way to improve energy efficiency and promote distributed energy utilization. IEM systems acquire electricity and gas from external markets and supply electricity/heat/cold to users. In this paper, we study the optimal energy purchase strategy for IEM, considering the impact of demand response incentives. Firstly, considering the uncertainties, we construct an IEM medium- and long-term market multi-energy purchase model based on conditional value-at-risk, optimizing the portfolio of electricity and gas purchases, as well as their proportion in total energy amount. Subsequently, based on medium- and long-term daily energy supply curves and day-ahead load forecast results, a spot market energy purchase model is established to optimize the spot purchase of electricity and gas, maintaining the supply-demand balance while minimizing operating costs. Furthermore, we design demand response incentives and develop a master-slave game model between IEM and users to guide the formulation of the energy purchase strategy by incorporating corrected load data as feedback. The energy purchase strategies are resolved by the GUROBI solver, while the optimization of demand response incentives is carried out through the PSO algorithm, all based on the MATLAB platform. The adaptability of the proposed model and strategy is verified.