This paper presents an approach to determine the vulnerable components in the electricity and natural gas networks of an islanded microgrid that is exposed to deliberate disruptions. The vulnerable components in the microgrid are identified by solving a bi-level optimization problem. The objective of the upper-level problem (the attacker’s objective) is to maximize the expected operation cost of microgrid by capturing the penalties associated with the curtailed electricity and heat demands as a result of the disruption. In the lower-level problem, the adverse effects of disruptions and outages in the electricity and natural gas networks are mitigated by leveraging the available resources in the microgrid (the defender’s objective). The uncertainties in the electricity and heat demand profiles were captured by introducing scenarios with certain probabilities. The formulated bi-level optimization problem provides effective guidelines for the microgrid operator to adopt the reinforcement strategies in the interdependent natural gas and electricity distribution networks and improve the resilience of energy supply. The presented case study shows that as more components are reinforced in the interdependent energy networks, the reinforcement cost is increased and the expected operation cost as a result of disruption is decreased.