A unified optimal power flow (OPF) model for AC/DC grids integrated with natural gas systems is proposed for the real-time scheduling of power systems. Herein, the primary physical couplings underlying this coordinated system are modeled and investigated. In addition, the uncertainties of gas loads are considered when studying the role of gas supply for gas-fired units in power system operations. The nonlinear gas system constraints are converted to the second-order cone forms that allow for the use of the Benders decomposition techniques and the interior-point method to obtain the optimal solution. The numerical results of the modified IEEE 118-bus test system that integrates the Belgium 20-node natural gas system demonstrate the effectiveness of the proposed model. The effects of gas demand uncertainties on the optimal schedule of thermal generators are investigated as well.