With the change of users’ energy consumption concept, the users are no longer rigid as the traditional inelasticity but can be flexible to carry out integrated demand response (IDR). The load has also been transformed from a traditional purely consumptive load to a new type of load that combines production and consumption with the improvement and popularization of renewable energy production technologies such as wind power and photovoltaic. In this paper, considering the IDR of loads and the uncertainty of renewable energy output, a decentralized robust optimal dispatch study is conducted on user-level integrated electricity-gas-heat systems (IEGHSs) composed of energy hubs (EHs) and some users. This paper firstly developed the comprehensive model of the user-level IEGHS, including the detailed mathematical model of EH, IDR, and users. Then, based on the established model, an optimal dispatching model is established with the goal of the lowest operating cost for the system. In order to cope with the uncertainty of the output of renewable energy equipment while protecting the security and privacy of different participants in the integrated energy system (IES), a decentralized robust algorithm is used to solve the model. Finally, the proposed model is analyzed and verified by an IES example composed of one EH and three users with the ability of IDRs, and the feasibility of the proposed model and algorithm is verified.