This paper presents a stochastic framework for day-ahead scheduling of microgrid energy storage systems in the context of multi-objective (MO) optimization. Operation cost of microgrid in normal conditions and load curtailment index in case of unscheduled islanding events (initiated by disturbances in the main grid) are chosen as main criteria of the proposed scheme. In practice, duration of disconnection from the upstream network is unknown in unscheduled islanding incidents and cannot be predicted with certainty. To properly handle the uncertainties associated with time and duration of such events as well as microgrid load and renewable power generation, stochastic models are involved in the MO scheduling framework and they are formulated as mixed integer linear programming problems. The non-dominated sorting genetic algorithm II is employed to effectively cope with the MO optimization problem and a fuzzy decision making approach is employed for appropriate representation of microgrid operator's preferences in compromising between the two objectives. The proposed scheme is implemented on a test microgrid and the obtained results demonstrate the applicability and efficiency of this framework in dealing with conflicting requirements of microgrid security and economic operation.