Critical infrastructures (CIs), such as energy systems, transportation networks and telecommunications networks, are the backbone of any advanced society, and ensuring their resilience is a fundamental task. CIs are often interconnected to, and interdependent on, each other through complex coupling interfaces. Failures can propagate among different CIs through these coupling interfaces, causing multi-sectoral disruption. The design of the coupling interface can strongly impact the cascading effect between different CIs. In this paper, we propose a data-driven distributionally robust approach for the optimal coupling of interdependent CIs. Our model obtains an optimal coupling interface that maximizes the expected combined performance of interdependent CIs under random failure scenarios with ambiguous probability distributions. We demonstrate the validity of the proposed approach using an ambiguity set built upon a synthetic data set of historical contingency scenarios. Interdependent power and gas networks (IPGNs) are used as an illustrative case study. We show that our proposed approach leads to better coupling interfaces with higher expected performance under disruptive scenarios.