Interdependent critical infrastructures (ICIs) that could trigger cascading impacts on one another have attracted great attention from academia. Most of the current studies regarding ICIs solely apply a data-driven method (e.g., inoperability input-output method) or a physics-based approach (e.g., topology network) to uniformly characterize disparate infrastructures. This manipulation not only often encounter the problem of lacking empirical data or physical knowledge as required by a designated method for depicting certain infrastructures, but also it may significantly ignore the heterogeneities of infrastructures in terms of operation mechanisms, failure characteristics, and measurement indicators. These challenges debilitate the adoption of a consistent model to characterize different infrastructures, hence a framework that can agilely integrate diverse data-driven methods and physics-based approaches is proposed to help demystify the failure propagation among interdependent infrastructures. The proposed framework consists of three major modules, including (i) understanding the basic profiles of each target infrastructure, (ii) selecting an applicable data-driven method or physics-based model to characterize each infrastructure system, and (iii) designing interfaces to operationalize the interdependencies between different infrastructures and to connect the selected methods through associated variables or parameters. Taking the geographically interdependent water supply system and road transport network as a case, the practicability of the proposed framework is demonstrated. The failure patterns of the water supply system in Hong Kong, including the hotspots, high-incidence time, and potential consequence types, were derived by mining news related to water pipe burst incidents. The cascading impacts caused by water pipe bursts on the road transport network, such as performance degradations revealed by traffic densities and vehicle delays, were further captured through physical traffic flow simulation. The developed integration framework shall contribute to the existing ICI research domain by increasing the flexibility of selecting applicable methods for individual infrastructures depending upon the availability of real-world data and physical models. Moreover, it could facilitate the retention and exploration of infrastructures’ heterogeneous features as desired by decision-makers in specific ICI research scenarios.