Epitaxial graphene on SiC provides both an excellent source of high-quality graphene as well as an architecture to support its application. Although single-layer graphene on Si-face SiC has garnered extensive interest, many-layer graphene produced on C-face SiC could be significantly more robust for enabling applications. Little is known, however, about the structural properties related to the growth evolution at the buried interface for thick many-layer graphene. Using complementary X-ray scattering and neutron reflectivity as well as electron microscopy, we demonstrate that thick many-layer epitaxial graphene exhibits two vastly different length-scales of the buried interface roughness as a consequence of the Si sublimation that produces the graphene. Over long lateral length-scales the roughness is extremely large (hundreds of Å) and it varies proportionally to the number of graphene layers. In contrast, over much shorter lateral length-scales we observe an atomically abrupt interface with SiC terraces. Graphene near the buried interface exhibits a slightly expanded interlayer spacing (∼1%) and fluctuations of this spacing, indicating a tendency for disorder near the growth front. Nevertheless, Dirac cones are observed from the graphene while its domain size routinely reaches micron length-scales, indicating the persistence of high-quality graphene beginning just a short distance away from the buried interface. Discovering and reconciling the different length-scales of roughness by reflectivity was complicated by strong diffuse scattering and we provide a detailed discussion of how these difficulties were resolved. The insight from this analysis will be useful for other highly rough interfaces among broad classes of thin-film materials.