A multi-energy microgrid (MEMG) aims to simultaneously supply electricity and thermal energy to customers for higher energy utilisation efficiency. In this study, a system-wide coordinated operation method for MEMGs is proposed to dispatch different components including generation resources and flexible loads. In the coordination method, the coupling constraints of electrical and heat network, dynamic characteristics of heat network as well as the power flow constraints are comprehensively modelled. Besides, the price-based demand response and indoor temperature control strategy are used as demand response for more flexible operation of the combine electrical and thermal networks. The coordination model is formulated as a mixed-integer linear programming problem and tested on 33-bus and 69-bus MEMGs. Simulation results verify the advantages of the proposed method over existing methods.