<p>Coupled multidisciplinary analysis (MDA) is a challenging task due to the presence of bidirectional coupling between individual disciplines, and these challenges multiply when uncertainty is associated with the input parameters of the individual disciplines. Uncertainty in input parameters can be of two types—aleatory and epistemic. Although several MDA methods under aleatory uncertainty are available in the literature, MDA methods under epistemic uncertainty are very few. This paper proposes a likelihood-based unified probabilistic framework to perform coupled MDA in the presence of input parameters having both aleatory and epistemic uncertainty. The focus of the paper is limited to a specific type of epistemic uncertainty—interval uncertainty that appears in the input parameters described by either multiple intervals or a mixture of discrete points and/or multiple intervals. The proposed framework exploits the worst-case maximum likelihood estimation (WMLE) method to quantify the interval uncertainty in the uncertain input parameter and the likelihood-based multidisciplinary analysis (LAMDA) method to perform coupled multidisciplinary analysis of the complex systems. It estimates the probability distribution of one of the coupling variables that partially decouples the complicated coupled multidisciplinary systems, thereby paving the way for estimating the probability distributions of other coupling variables, subsystem outputs, and system outputs. A numerical problem and a complex real-life engineering problem (fire detection satellite) are used to demonstrate the proposed uncertainty quantification framework. Results (in terms of statistics of the coupling variables, subsystem, and system outputs) and computational efforts (in terms of the number of disciplinary analyses) in solving the mentioned problems are compared with an earlier study.</p>