At early design phases, taking into account uncertainty in the optimization of a multidisciplinary system is essential to assess the optimal characteristics and performance. Uncertainty multidisciplinary design optimization methods aim at efficiently organizing not only the different disciplinary analyses, the uncertainty propagation, and the optimization but also the handling of interdisciplinary couplings under uncertainty. A new decoupled uncertainty multidisciplinary design optimization formulation (named Individual Discipline Feasible/Polynomial Chaos Expansion) ensuring the coupling satisfaction for all the realizations of the uncertain variables is presented in this paper. Coupling satisfaction in realizations is necessary to maintain the equivalence between the coupled and decoupled uncertainty multidisciplinary design optimization formulations, and therefore to ensure the physical relevance of the obtained designs. The proposed approach relies on the iterative construction of Polynomial Chaos Expansions in order to represent, at the convergence of the optimization problem, the functional couplings between the disciplines. The proposed formulation is tested on an analytic problem and on the design of a two-stage launch vehicle.