As the ultimate users and cost-bearers of power systems, consumers experience significant consequences from widespread, long duration power interruptions caused by extreme weather events. Therefore, it is crucial to integrate their perspectives in power system resilience assessments. Yet, existing power system resilience definitions, metrics and assessment frameworks primarily focus on technical perspectives. This work attempts to address the above-mentioned limitation by proposing a dual-focused approach for resilience assessments. We analyze both technical and consumer viewpoints, identify similarities and differences between reliability and resilience, and propose a refined definition of power system resilience that incorporates both perspectives. By modifying conventional distribution system reliability indices, metrics are proposed to assess resilience from both technical and consumers' viewpoints. Capability of ensuring social equity through the utilization of proposed metrics is highlighted. A case study is conducted using past data to illustrate the applicability of proposed metrics. Furthermore, a framework is developed for probabilistic resilience assessments of future power systems, utilizing the proposed dual perspective metrics. © 2024 IEEE.