This paper discusses microgrid power supply resiliency in extreme events and the impact of power electronic interfaces, energy storage, lifelines, and the characteristics of distribution architectures. Resiliency is characterized based on metrics analogous to those of availability considering the presence of power electronic interfaces and energy storage. The effect of energy storage on microgrid resiliency is analyzed and resiliency improvement in the presence of diverse sources is discussed. Resiliency metrics, which are time dependent in nature, are derived under natural disasters conditions. Resiliency is calculated for microgrids containing photovoltaics with batteries, diesel generators, and fuel storage with discontinuous fuel supply. Hurricane conditions are considered to provide a practical context for the discussion. Microgrid resiliency formulas are derived for radial, ring, and ladder architectures. It is shown that the resiliency formula for radial architecture can be used as a building block to derive the formulas for the ring and ladder networks. Architecture resiliencies are compared in islanded and grid-tie modes. The results indicate that the effects of including energy storage and source diversity, such as combinations of renewable energy sources and diesel generators, can improve power supply resiliency when the microgrid is in island mode, which is the most likely operating mode during extreme events.