In this work we introduce a mixed integer linear program (MILP) for multi-layer networks with demand uncertainty. The goal is to minimize the overall network equipment costs containing basic node costs and interface costs while guarding against variations of the traffic demand. Multi-layer network design requires technological feasible inter-layer connections. We present and evaluate two layering configurations, top-bottom and variable. The first layering configuration utilizes all layers allowing shortcuts and the second enables layer-skipping. Technological capabilities like router-offloading and layers able to multiplex traffic demand are also included in the model. Several case studies are carried out applying the Γ-robustness concept to take into account the demand uncertainties. We investigate the dependency of the robustness parameter Γ on the overall costs and possible cost savings by enabling layer-skipping.