Water affordability is an emerging problem as aging infrastructure and climate change uncertainty lead to rising water prices. In California alone, over one million people currently lack access to safe, affordable drinking water. Currently, utility-level water supply planning practices focus on meeting system-level reliability under hydrological sources of uncertainty, such as drought and climate variability, for a minimal cost to the utility. This systems-level aggregation does not consider how utility-level decisions have varying impacts on different households, with implications for distributional equity. We develop a decision-support tool to explicitly incorporate household affordability metrics into utility-level water supply planning. The goal of our model is to understand what utility-level infrastructure and policy options improve affordability under different future scenarios. Our model integrates future hydrological scenarios; utility-level rate design, infrastructure investment, and policy options; and household water-use behavior across income and housing groups. We use multi-objective optimization methods to understand tradeoffs between household affordability, utility cost recovery, and water reliability. We apply our model to the City of Santa Cruz, a coastal city in California reliant on local surface water supplies that is vulnerable to climate change and includes diverse socioeconomic populations. Our work aims to improve the understanding of distributional equity implications for water supply planning under climate change and develops the first utility-level decision-support tool that explicitly incorporates and optimizes for household affordability impacts.