Due to the presence of combined heat and power plants (CHP) and thermostatically controlled loads, heat, natural gas and electric power systems are tightly coupled in community areas. However, the coordination among these systems has not been well considered, especially with the integration of renewable energy. This paper aims to develop a hierarchical approach for an integrated community energy system (ICES). The proposed hierarchical framework is presented as day-ahead scheduling and two-layer intra-hour adjustment systems. Two objectives, namely operating cost and tie-line power smoothing, are integrated into the framework. In the intra-hour scheduling, a master-client structure is designed. The CHP and thermostatically controlled loads are coordinated by a method with two different time scales in order to execute the schedule and handle uncertainties from the load demand and the renewable generation. To obtain the optimal set-points for the CHP, an integrated optimal power flow method (IOPF) is developed, which also incorporates three-phase electric power flow and natural gas flow constraints. Furthermore, based on a time priority list method, a three-phase demand response approach is proposed to dispatch HVACs at different phases and locations. Numerical studies confirm that the ICES can be economically operated, and the tie-line power between the ICES and external energy network can be effectively smoothed.