Objective: As urbanization accelerates and climate change intensifies, the risks of various urban disasters have increased considerably, hindering the transition toward urban resilience. As the core carrier of urban operation, urban infrastructure plays a pivotal role in enhancing urban resilience. Analyzing the interactions and correlation characteristics within its flood control system is of great importance for risk identification and resilience building in urban systems. Previous research on urban resilience has primarily focused on statistical methods, with limited research analyzing the characteristics of urban resilience from a probabilistic perspective. The Copula joint probability method offers distinct advantages in exploring multidimensional nonlinear relationships in complex systems and conducting comprehensive probability assessments of interfactor interactions. Methods: This study developed an evaluation index system for urban infrastructure flood resilience (UIFR) based on the resistance R–adaptability A–recovery C framework. The study used survey data from 2000 to 2022 and employed a Copula-theory-based joint probability estimation approach to characterize the correlation patterns among UIFR dimensions and the comprehensive probability of multifactor joint effects. In addition, the Copula function model was applied to investigate the joint distribution probability of UIFR in the Beijing–Tianjin–Hebei region of China, which is frequently affected by floods. The eXtreme gradient boosting-SHapley additive explanations (XGBoost–SHAP) model was integrated to explore the driving effects on UIFR. Results: The results showed that: 1) from 2000 to 2022, the UIFR in the Beijing–Tianjin–Hebei region exhibited fluctuating changes with an overall upward trend. Beijing recorded the highest UIFR, followed by Tianjin, while Hebei Province ranked the lowest. 2) For the two-dimensional joint distribution probability, the probability of achieving high resilience for the A–C pair in Beijing was 0.761 9, whereas the highest probabilities of high resilience for the R–A pair in Tianjin and Hebei were 0.116 9 and 0.149 7, respectively; the lowest probability of high resilience for the A–C pair in Hebei was 0.063 4. 3) For the three-dimensional joint distribution probability, the probabilities of achieving high resilience for the R–A–C combination in Beijing, Tianjin, and Hebei were 0.717 2, 0, and 0.066 2, respectively. The unbalanced development among UIFR dimensions impaired the overall level of the UIFR. 4) The harmless domestic waste treatment rate C₅, per capita urban electricity consumption R₄, and the share of the labor force A4 had remarkable impacts on the UIFR in the Beijing–Tianjin–Hebei region, with strong interaction between C₅ and other factors. The complex interactions among factors jointly influenced the UIFR in the Beijing–Tianjin–Hebei region. Conclusions: The UIFR joint probability method based on Copula functions demonstrates strong linear correlations between theoretical and empirical probability values of each Copula function, enabling effective two-dimensional and three-dimensional joint probability assessments of urban resilience. This method offers a new perspective on the relationships between internal connectivity and different aspects of resilience in UIFR. In addition, this study identifies key risk factors affecting the UIFR improvement in the Beijing–Tianjin–Hebei region, proposing additional targeted policy recommendations for future urban resilience initiatives. This study provides data support and theoretical guidance for joint risk assessment within infrastructure flood resilience systems and the coordinated development of urban resilience.