Reliability enhancement is a major motivation for integrating electric and gas energy distribution systems. Compared with reliability assessment at the stage of planning, which emphasizes calculating the system annual average indices, the coupling of gas and electric energy flows contributes more to the operational reliability of the integrated system, especially during peak-load periods. In this paper, a method is proposed that assesses system outage risk in each time period by modeling the consequence of the worst N-1 fault in the integrated electric-gas system. In order to accurately model the load transfer process, a novel dynamic load restoration model is applied to minimize load loss of the system, where the fluctuation of multiple energy flows during fault clearing periods is considered. The effectiveness of the proposed approach is validated by performing case studies.