Multi-energy systems (MES) allow various energy forms, such as electricity, gas, and heat, to interact and achieve energy transfer and mutually benefit, reducing the probability of load cutting in the event of a failure, increasing the energy utilization efficiency, and improving the reliability and robustness of the overall energy supply system. Since energy storage systems can help to restore power in the case of failure and store the surplus energy to enhance the flexibility of MES, this work provides a methodology for reliability optimization, considering different energy storage configuration schemes under weather uncertainties. First of all, a reliability evaluation model of a multi-energy system under weather uncertainties based on a sequential Monte Carlo simulation is established. Then, the reliability optimization problem is formulated as a multi-objective optimization problem to minimize the reliability index, SAIDI (system average interruption duration index), and the reliability cost. Finally, a case study implemented on a typical MES layout is used to demonstrate the proposed methodology. A comparative analysis of three widely adopted multi-objective metaheuristic algorithms, including NSGA-II (non-dominated sorting genetic algorithm II), MOPSO (multiple objective particle swarm optimization), and SPEA2 (strength Pareto evolution algorithm 2), is performed to validate the effectiveness of the proposed method. The simulation results show that the NSGA-II algorithm leads to better optimal values and converges the fastest compared to the other two methods.