Climate vulnerability assessments have traditionally relied on macro-level indices and physical exposure models, overlooking household-level heterogeneity and the behavioral determinants of vulnerability. To fill this gap, we develop a general, replicable Climate Vulnerability Index (CVI) that measures climate vulnerability at the household level by integrating experience-based exposure, sensitivity, and behavioral adaptive capacity, including risk preferences, time preferences, climate knowledge, and observed adaptive behaviors, into the established IPCC vulnerability framework. The index classifies households into Low, Stress, Crisis, and Emergency categories of climate vulnerability based on a transparent hierarchical logic. Second, we apply this framework to the 2024 UNHCR Vulnerability Assessment Framework (VAF) in Jordan, a representative survey of the UNHCR-registered refugee population (N = 5,164 refugee households), producing the first behaviorally informed climate vulnerability profile of a national refugee population. Approximately 40 percent of households fall into concerning vulnerability categories and roughly 10 percent are classified as Emergency, with camp-based refugees systematically more vulnerable than those in host communities. Two validation exercises comparing self-reported exposure with objective climatic indicators and benchmarking the CVI against an independent national vulnerability mapping reveal that the household-level index captures dimensions of lived climate risk invisible to aggregate assessments. These findings underscore the value of integrating micro-level and behavioral dimensions into climate vulnerability measurement to improve targeting, anticipatory action, and resilience programming for displaced populations.