Resilience of power systems is already a key issue that is getting frequent attention all over the world. It is useful to analyze resilience issues not only for bulk supply, but at all levels including at a customer level. This is because distributed energy resources can play a prominent role in enhancing resilience. Although the literature on planning models, tools and data for bulk supply and distribution systems have expanded in recent years, customer-centric planning, e.g., for an individual household, is yet to receive adequate attention. Although solar PV and battery storage at a household level have been analyzed, how these resources can be optimally combined, together with grid supply, from a resilience perspective is the focus of this study. The study demonstrates how a conceptual framework can be developed to show the trade-off between system costs and resilience including its dimensions such as duration, depth and frequency of service outages. A planning model is developed that incorporates multiple facets of resilience and individual customer preferences. The model considers power system resilience explicitly as a constraint. The model is implemented for a household level case study in Miami, Florida. The results show there are complex tradeoffs among different dimensions of resilience. The study demonstrates how combined resilience metrics can be formulated and evaluated using the proposed least-cost planning model at a household level to optimize grid supply together with solar, battery storage and diesel generators. The model allows a planner to directly embed a resilience standard to drive the optimal supply mix. These concepts and the modeling construct can also be applied at other levels of planning, including community level and bulk supply system planning.