This work investigates the extension of non-intrusive local/global coupling methods to multiscale robust design optimization. Indeed, industrial structures are commonly described by hierarchies of interconnected models, requiring consistent information exchange across scales. Classical top-down design strategies often account for the impact of local modeling uncertainties on global performance through safety factors, which may lead to overly conservative or insufficiently robust solutions. A bidirectional robust design framework is proposed to explicitly incorporate local variabilities and uncertainties at early design stages. The approach relies on a non-intrusive local/global coupling strategy, in which a coarse global finite element model is enriched by localized patches capturing fine-scale effects, without altering its intrinsic parameters. Interface quantities are exchanged iteratively between global and local models, ensuring multiscale consistency while preserving compatibility with industrial solvers. A major challenge addressed in this work concerns the efficient propagation of uncertainties across scales. Two distinct sources of variability are considered: random local uncertainties, representing intrinsic physical variability, and epistemic global uncertainties associated with design variables targeted by robust optimization. To efficiently handle this coupled uncertainty structure, a hybrid surrogate modeling strategy is introduced. The impact of local uncertainties on the global stochastic response is represented using Polynomial Chaos Expansion, while the dependence of the chaos coefficients on the global design variables is approximated by kriging. This hybrid metamodel enables efficient uncertainty quantification and reduced-cost exploration of the design space. The resulting surrogate model is integrated within a multi-objective robust optimization framework based on the NSGA-II algorithm. The methodology is applied on typical examples characterized by strong sensitivity to geometric perturbations, highlighting the relevance of the proposed approach for multiscale robust design.