With the coordination of multiple energies at the city level, the complexity of the urban energy system is ever-increasing. Securing the reliable operation of the urban multi-energy system (UMES) has become a challenging task. This article focuses on the operational reliability evaluation of the UMES considering the incorporation of equivalent energy storages. First, a novel concept of dynamic energy hub is proposed, as a unified tool to characterize the dynamic relationships of the operating conditions of diverse components in the UMES. Then, the temperature-controlled load (TCL) is modeled as the equivalent energy storage considering the thermal dynamics. Its operational reliabilities, as well as multiple other components, are modeled using the reliability equivalent technique to reduce the dimension of uncertainties. Moreover, a contingency management scheme of the UMES is developed in an optimal control framework considering the comfort costs of equivalent energy storages. To deal with the time-dependency of the optimal control problem, a simplified Benders decomposition procedure is devised and embedded in the Time-sequential Monte Carlo simulation to improve the computation efficiency of the reliability evaluation. Finally, a practical case of a UMES in southern China is used to validate the proposed technique.