In view of the issues that the current comprehensive energy supply reliability evaluation mainly focuses on the distributed energy system and rarely involves the mutual coupling of energy supply networks and the coordination of energy stations in the regional energy Internet, an evaluation method of energy supply reliability considering electricity-gas coupling and coordination between energy stations was proposed. First, the framework of regional energy Internet (REI) is established, the energy flow relationship among the main parts in the REI and the influence of electricity-gas coupling on reliability are analysed; second, considering building virtual energy storage and demand response, the rigid and flexible reliability evaluation indexes are proposed from the energy and time levels; third, the operation strategies of normal, failure and repair periods of each energy station are put forward, and the optimal load reduction model of REI aiming at the minimum total rigid energy shortage is established. Moreover, the method and process of energy supply reliability evaluation combining fault mode effect analysis (FMEA) and Monte Carlo simulation are proposed. Finally, through a practical example, the impact of demand response, multiple energy storage resources, electricity-gas coupling and interstation coordination on reliability is analysed.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.