Coordinated multi-carrier energy systems with natural gas and electricity energies provide specific opportunities to improve energy efficiency and flexibility of the energy supply. The interdependency of electricity and natural gas networks faces multiple challenges from power and gas flow in corresponding feeders and pipes and connection points between two infrastructures’ points of view. However, the energy hub concepts as the fundamental concept of multi-carrier energy systems with multiple conversion, storage, and generation facilities can be considered as a connection point between electricity and gas grids. Hence, this paper proposes an optimal operation of coordinated gas and electricity distribution networks by considering interconnected energy hubs. The proposed energy hub is equipped with combined heat and power units, a boiler, battery energy storage, a heat pump, and a gas-fired unit to meet the heating and electrical load demands. The proposed model is formulated as a two-stage scenario-based stochastic model aiming to minimize total operational cost considering wind energy, electrical load, and real-time power price uncertainties. The proposed integrated energy system can participate in real-time and day-ahead power markets, as well as the gas market, to purchase its required energy. The AC-power flow and Weymouth equation are extended to describe power and gas flow in feeders and gas pipelines, respectively. Therefore, a realistic model for the integrated electricity and gas grids considering coupling constraints is satisfied. The proposed model is tested on the integrated energy system and consists of a 33-bus electrical network and a 6-node gas grid with multiple interconnected energy hubs, where the numerical results reveal the effectiveness of the proposed model.