Existing distribution network resilience assessments mostly focus on the total amount or proportional of load loss, an evaluation paradigm that fails to reflect the loss of urban social functions caused by load shedding. To address this limitation, and oriented toward urban social function demands during disasters, a resilience assessment method for distribution networks under earthquake disasters is proposed by considering the operational coupling of water supply, power distribution, and gas supply systems, as well as the uncertainty of earthquake events. First, from the three dimensions of water-electricity-gas supply adequacy, severity of building damage, and urgency of urban social function demands, urban social function losses under earthquake scenarios are comprehensively assessed. Next, with the objective of minimizing urban social function loss, a load shedding model for distribution networks is formulated by incorporating the coupling constraints among water, power, and gas networks, together with their respective operational constraints. This model optimizes the supply of these resources under earthquake scenarios to best satisfy urban social function demands. Finally, considering the uncertainty in earthquake magnitude and spatial distribution, the resilience of distribution networks under earthquake disasters is evaluated using the expected urban social function loss as the metric. Case study results demonstrate that the proposed method overcomes the limitations of existing “electric power and energy loss”-based assessments, more accurately captures the core supporting role of distribution systems in urban social functions, and effectively enhances the level of urban social functions under earthquake disasters.