Optimal configuration of various types of energy storage is beneficial for reducing the fluctuation of renewable energy and for improving the reliability and economy of energy consumption in the multi-energy microgrid. Taking a multi-energy microgrid with wind power, photovoltaic generation and electricity/thermal/gas load as the study object, this paper studies the optimal allocation of multiple energy storage systems in a multi-energy microgrid considering electricity/thermal/gas coupling demand response. First, the coupling demand response model is built based on the ambiguity of body to temperature and the transferable characteristics of electricity and gas load. Based on the coupling demand response, in order to minimize economic cost and carbon emissions, a multi-objective optimization model is proposed where coupling demand response and different energy storage is taken into account. After that, in order to deal with the flexibility of the planning scenario, an adaptive dynamic weight factor is used. Finally, the economic cost and carbon emissions of the multi-energy microgrid before and after the application of coupling demand response and the configuration of the energy storage system are compared through a case study. This verifies the effectiveness of the proposed method. This work is supported by the Sichuan Science and Technology Program (No. 2019YFG0152) and National Key Research and Development Program of China (No. 2018YFB0905200).