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Driven by the goal of ‘carbon peak, carbon neutrality’, an integrated demand response strategy for integrated electricity–hydrogen energy systems is proposed for low-carbon energy supply parks considering the multi-level and multi-energy characteristics of campus-based microgrids. Firstly, considering the spatial and temporal complementary nature of wind and photovoltaic generation and energy utilization, the energy flow framework of the park is built based on the electricity and hydrogen energy carriers. Clean energy is employed as the main energy supply, and power, heat, cooling, and gas loads are considered energy consumption. Secondly, the operation mechanism of coupled hydrogen storage, hydrogen fuel cell, and carbon capture equipment is analyzed in the two-stage power-to-gas conversion process. Thirdly, considering the operating costs and environmental costs of the park, an integrated demand response dispatch model is constructed for the coupled electricity–hydrogen–carbon system while satisfying the system equipment constraints, network constraints and energy balance constraints of the park system. Finally, Case study in an energy supply park system is implemented. The dispatch results of the integrated demand response with customer participation in the conventional, electricity–hydrogen and electricity–hydrogen–carbon modes are compared to verify the effectiveness of the proposed strategy in renewable accommodation, environmental protection, and economic benefits.