Integrated energy microgrids and shared energy storage have significant benefits in improving the energy utilization of the system, which is gradually becoming the current research hotspot. And the uncertainty of new energy output also significantly affects the stable and economic operation of integrated energy microgrid. So how to establish a set of integrated energy microgrids optimization operation model considering photovoltaic (PV) output uncertainty and shared energy storage is an urgent problem to be solved nowadays. Firstly, this paper introduces the framework of an integrated energy system microgrid containing a shared energy storage operator (ESO), and analyzes the scheduling method of the upper tier operator within the system as well as the economic benefits at the lower tier user end. Secondly, to address the randomness of PV output, Monte Carlo method is used to generate the scenarios, and then the scenarios are cut down by using the fast antecedent elimination technique. Then, an optimal operation model is established for micro grid operator (MGO) and user aggregator (UA), respectively, and based on the master-slave game relationship, so that the MGO is the leader and the UA is the follower, a Stackelberg game model is proposed to consider the integrated demand response of electricity and heat between the MGO and UA in the context of the participation of ESO in the auxiliary service of the UA. Finally, the proposed model is brought into a typical residential building community for simulation verification, and the results show that the model proposed in this paper can effectively balance the interests of MGOs and UAs, and realize win-win benefits for UA and ESO.