Dealing with major power disruption during natural disasters is one of the most notable concerns in power systems. In this regard, the optimal application of microgrids as a potential solution in increasing and sustaining the distribution system resilience is considered. Furthermore, this purpose is pursued while maintaining the resilience of each DC microgrid connected to the distribution system, which is an essential and challenging issue. In the proposed method of this paper, a novel modeling strategy is formulated as a multi-period two-stage scenario-based stochastic mixed-integer linear programming (MPTSS-MILP) based on a multi-objective optimization problem (MOOP). In this framework, the operation associated with emergency and normal conditions, according to the influences of each situation on another one, is managed in multi-microgrids coordinately. In this regard, the technical constraints correlated to the operation of microgrids as well as the distribution system are satisfied simultaneously in specific to each condition which covers normal and critical operating under all uncertainty scenarios. Through introducing two evaluation criteria and also a resilience metric in microgrids and distribution systems, the efficiency of the proposed method is demonstrated. Meanwhile, innovative modeling is executed based on the subjective behavior of people affected by the disaster. The proposed method is implemented on a test system that involves a 34-bus distribution system with three distinct DC microgrids. In this regard, the impact of plug-in electric vehicles, as well as social behavior affected by severe events, demonstrate significant results according to the resilience criteria and resilience metric of microgrids and distribution system in three case studies based on the proposed approach.