Sustainability and resilience of urban systems are multifaceted concepts, requiring information about multiple system attributes to adequately evaluate and characterize. However, despite the scientific consensus on the multivariate nature of these concepts, many of the existing techniques to model urban sustainability and resilience are unidimensional in nature, focusing on a characterizing a single element of highly interconnected urban systems. We champion a paradigm shift in modeling urban sustainability and resilience, using an integrated approach to simultaneously estimate multiple interconnected (correlated) system attributes of sustainability and resilience as a function of key environmental factors. We present a novel case study and review a few recent studies to illustrate the applicability and benefits of the multivariate approach to modeling urban sustainability and resilience. Our proposed framework can be utilized by infrastructure managers, urban planners, and researchers to conceptualize and assess urban sustainability and resilience more holistically, and to better understand the key factors in advancing the sustainability and resilience of infrastructure systems.