The intercalation of various atomic species, such as hydrogen, to the interface between epitaxial graphene (EG) and its SiC substrate is known to significantly influence the electronic properties of the graphene overlayers. Here, we use high-resolution X-ray reflectivity to investigate the structural consequences of the hydrogen intercalation process used in the formation of quasi-free-standing (QFS) EG/SiC(0001). We confirm that the interfacial layer is converted to a layer structurally indistinguishable from that of the overlying graphene layers. This newly formed graphene layer becomes decoupled from the SiC substrate and, along with the other graphene layers within the film, is vertically displaced by ∼2.1 Å. The number of total carbon layers is conserved during the process, and we observe no other structural changes such as interlayer intercalation or expansion of the graphene d-spacing. These results clarify the under-determined structure of hydrogen intercalated QFS-EG/SiC(0001) and provide a precise model to inform further fundamental and practical understanding of the system.