The coupling of various energy sources in each link of the integrated energy system (IES) is becoming stronger and stronger. An operation framework of community integrated energy system (CIES) considering the bilateral cross coupling of energy supply and demand is created, and the refined mathematical model of energy coupling equipment considering the variable working conditions is established. Then, the electric thermal coupling demand response mechanism based on the Price-Demand elasticity model is established, and a bi-level optimization model which considering the maximum revenue of the Source-side Energy Station (SSES) and the minimum energy consumption offset of the Load-side Users (LSU) is proposed. In order to transform the bi-level model into a single-layer model of mixed integer linear programming, the piecewise linearization technology, karush Kuhn Tucker (KKT) technology and duality theorem are applied. Finally, the optimal equilibrium strategy is obtained and the simulation results show that the mechanism and model proposed in this paper are feasible and superior.