As critical infrastructures (CIs) are essential for the safety and socio-economic stability of a society, ensuring their resilience is a task of the utmost importance. Critical infrastructures are often interdependent on each other, and the topology of the interdependencies between different systems, also referred to as coupling interface, plays a key role in terms of their resilience against failures. In case of failures due to natural events, random disturbances, or deliberate attacks, the design of the coupling interface is a key factor for maintaining high performance within the interdependent CIs. However, in the existing literature, the issue of the coupling interface design is often addressed through heuristics. In this work, we propose an optimization-based mathematical approach for designing coupling interfaces between interdependent critical infrastructures under random failures. The proposed approach allows designing a coupling interface that is robust against the worst realization of a set of feasible failure scenarios. Using as case-study interdependent power and gas networks, we show that the proposed method outperforms existing solutions based on network metrics-based heuristics.