Reliable energy supply becomes increasingly complex in hybrid energy networks, due to increasing amounts of renewable electricity and more dynamic demand. Accurate modeling of integrated electricity and gas distribution networks is required to quantify operational bottlenecks in these networks and to increase security of supply. In this paper, we propose a hybrid network solver to model integrated electricity and gas distribution networks. A stochastic method is proposed to calculate the security of supply throughout the networks, taking into account the likelihood of events, operational constraints and dynamic supply and demand. The stochastic method is evaluated on a real gas network case study. The calculated security of supply parameters provide insight into the most critical parts of the network and can be used for future network planning. The capabilities of the coupled hybrid energy network simulation are demonstrated on the real gas network coupled to a simplified electricity network. Results demonstrate how combined simulation of electricity and gas networks facilitate the control design and performance evaluation of regional hybrid energy networks.