In order to promote the multi-energy coordination and mutual assistance of the integrated energy system（IES）and improve energy efficiency, taking the electricity-heat -gas（EHG）-IES as the research object, a multi-objective collaborative optimization integrated demand response（IDR）model and operation strategy solving algorithm are proposed. Firstly, EHG- IES architecture with IDR is designed, and the energy coupling matrix is used to describe the multi - energy conversion relationship in interconnected system. Under the time -sharing energy price mechanism, a multi energy coordinated IDR mathematical model with mixed time or space is constructed. Then, with the goal to minimize system energy cost, environmental cost, abandoning wind and optical power,an optimal dispatch model of environmental economy is constructed. The Co -NSGA -Ⅱ is used to solve this model. The simulation results show that the proposed model and optimal operation strategy can effectively promote the energy coordination ability and comprehensive demand response ability among multi-energy systems.