The mechanisms governing the formation of Schottky barriers at graphene/hydrogen-passivated silicon interfaces where the graphene plays the role of a two-dimensional (2D) metal electrode have been investigated by means of x-ray photoemission spectroscopy and density functional theory (DFT) calculations. To control the graphene work function without altering either the structure or the band dispersion of graphene we used a method that consists in depositing small amounts of gold forming clusters on the graphene/hydrogen-passivated silicon system under an ultra-high-vacuum environment. We observe from experimental measurements that the Fermi level is mainly free from pinning at the graphene/hydrogen-silicon interface whereas for a semi-infinite metal on silicon the Fermi level is almost fully pinned. This alleviation of the Fermi level pinning observed with the graphene layer is explained by DFT calculations showing that the graphene and the semiconductor are decoupled and that the metal-induced gap states (MIGS) density at the silicon midgap at the interface is very low ($l5\ifmmode\times\else\texttimes\fi{}{10}^{10}\phantom{\rule{0.16em}{0ex}}\mathrm{states}/(\mathrm{eV}\phantom{\rule{0.28em}{0ex}}\mathrm{c}{\mathrm{m}}^{2})$]. The important conclusion that stems from the DFT results analysis is that the low MIGS density at the semiconductor midgap is related to the 2D nature of the graphene layer. More precisely, the MIGS density is low owing to the lack of propagating states perpendicular to the graphene layer. This finding brings important information to understand the mechanisms that govern the formation and the electronic properties of Schottky barriers at 2D-metal/three-dimensional-semiconductor interfaces.