In regions heavily affected by recurrent typhoons, the need for more resilient electricity infrastructure is pressing. This emphasizes the importance of integrating resilience assessment, including incorporating resilience metrics, into the planning process of power distribution systems against any disruptive events. Although standardized metrics exist for assessing distribution system reliability, the absence of formalized resilience metrics hampers informed investments in critical infrastructure such as microgrid development. In this work, a set of resilience metrics is proposed by reconceptualizing reliability metrics. The metrics were formulated to account for both the type of extreme event and its specific impact on loads with varying levels of criticality. The effectiveness of the proposed metrics is demonstrated through a Philippine microgrid case study. A Monte Carlo framework incorporating an extreme event model, component fragility model, and system response model was used to quantify the resilience improvement before and after stand-alone microgrid operation of the power distribution system. Results show that the proposed metrics can effectively evaluate resilience enhancement and highlight the value of a holistic approach of considering critical loads and types of extreme events to strengthen societal and community resilience, making a compelling case for strategic investments in infrastructure upgrades such as microgrids.