To fully exploit the peak shaving potential of the multi-energy complementary system in a collaborative manner between energy supply and demand, this paper proposes an economic dispatch method for a multi-energy microgrid system that integrates demand response with heat pump technology. The introduction of natural gas heat pumps on the supply side enables energy substitution through multi-energy complementarity, effectively reducing the operating load of peak electricity demand from air conditioning equipment. On the demand side, the electricity price demand response is considered, incorporating user electricity satisfaction into the demand response model to optimize power demand based on user electricity consumption experience, achieving peak load shaving and off-peak load filling. The objective of the optimization is to minimize system operating costs, taking into account energy balance and demand response constraints, and solving the optimization problem using the CPLEX software. The case study demonstrates that the collaborative peak shaving between energy supply and demand can effectively reduce peak electricity demand, leading to improved economic efficiency of the system.