Resilience is mostly considered as a single-dimension attribute of a system. Most of the recent works on resilience treat it as a single-dimension attribute of a system or study the different dimensions of the resilience separately without considering its multi-domain nature. In this paper, we propose an advanced causal inference approach combined with machine learning to characterize the spatio-temporal and multi-domain vulnerability of an urban infrastructure system against extreme weather events. With the proposed causality approach, we perform vulnerability assessment for electricity outages and roadway closures through considering the meteorological, topographic, and demographic attributes of urban areas in the aftermath of the extreme weather events. This proposed holistic approach to multi-network vulnerability assessment paves the ground for characterizing the resilience in a multi-network scheme, which is coined as the concept of “co-resilience.” The proposed causal framework for multi-network vulnerability assessment is validated using the actual data for the impacts of the Hurricane Hermine 2016 and the January Storm 2017 on the Tallahassee, FL, USA. The results achieved from the proposed causality approach indicate a high causal relationship among electricity outages, roadway closures, topographic aspects, and meteorological variables in an urban area. Findings show that the proposed multi-network approach for vulnerability assessment improves the performance of the estimation and prediction of the disaster outcomes and the evaluation of the overall system resilience.