In co-scheduling of the integrated electrical energy and natural gas systems with high penetration of renewable energy sources, it is vital to have flexible resources to handle uncertainties, viz., continuous wind uncertainty and discrete equipment failures. Accordingly, this paper evaluates the effectiveness of electrical grid flexibility, i.e., optimal grid reconfiguration (OGR), on the scheduling plan of both energy systems. Also, to characterize the continuous/discrete uncertainty sources, this paper aims to develop a new computationally-efficient hybrid stochastic/IGDT (HS-IGDT) optimization framework for the co-scheduling of electrical energy and natural gas systems. Finally, the IEEE Reliability Test System with ten-node gas transmission system have been analyzed to show the efficiency of the proposed framework. (C) 2019 Elsevier Ltd. All rights reserved.