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According to Feeding America, prior to the pandemic, 1 in 5 African-American/Black, 1 in 6 Hispanic, and 1 in 4 Native American households were food insecure compared to 1 in 11 White households. The pandemic is expected to exacerbate these disparities given its disproportionate economic and health impact on historically marginalized racial and ethnic populations. Food banks are non-profit organizations that work to alleviate food insecurity within their service regions by distributing donated food to households in need. Equitable distribution of donated food is an important criteria for food banks. Existing food banking operations literature primarily focus on geographic equity, i.e., where each geographic block of a food bank's service region receives food in proportion to its demand. However, hunger-relief organizations such as food banks are gradually incorporating demography-based equity in their distribution of donated food in light of the disparities that exist within different demographic groups, such as race, age, and religion. However, the notion of demographic equity has not received attention in the food banking operations literature. This study aims to fill in the gap by developing a multi-criteria optimization model to identify optimal distribution policies for a food bank considering a two-dimensional equity criterion, geographic and demographic, in the presence of effectiveness (undistributed food minimization) and efficiency (distribution cost minimization) criteria. We apply the model to our partner food bank's data to (i) explore the trade-off between geographic and demographic equity as a function of effectiveness, and efficiency, and (ii) identify policy insights.