Current design strategies for multi-physics systems seek to exploit synergistic interactions among disciplines in the system. However, when dealing with a multidisciplinary system with multiple physics represented, the use of high-fidelity computational models is often prohibitive. In this situation, recourse is often made to lower fidelity models that have potentially significant uncertainty associated with them. We present here a novel approach to quantifying the discipline level uncertainty in coupled multi-physics models, so that these individual models may later be used in isolation or coupled within other systems. Our approach is based off of a Gibbs sampling strategy and the identification of a necessary detailed balance condition that constrains the possible characteristics of individual model discrepancy distributions. We demonstrate our methodology on both a linear and nonlinear example problem.