The growth and electronic structure of bilayer graphene (gr) on different substrates have attracted a lot of attention in the last years owing to the possibility of tuning the band gap in the electronic spectrum for the graphene π states around the K point. In the present study, the electronic structure of single- and double-layer graphene on Rh(111) is studied using different surface science methods accompanied by DFT calculations. It is shown that in the case of 1 ML-gr/Rh(111), the freestanding-like electronic structure of graphene is completely destroyed due to the strong interaction with the metallic substrate. For the 2 ML-gr/Rh(111) system, the AB (Bernal) stacking of graphene layers is found, leading to the restoration of the electronic structure for the top graphene layer, its n-doping, and opening of the band gap at the K point. These results lead to a deep understanding of the interaction mechanisms between multilayer graphene and metallic supports that can be used for better modeling of different graphene-based applications.