Although not an intrinsic superconductor, graphite exhibits superconductivity when intercalated with certain dopants. Perhaps the most studied of these graphite-based superconductors are the alkali metal-graphite intercalation compounds (GICs) (ref. 2), of which the easiest to fabricate is C8K (ref. 3), with a transition temperature (ref. 2). By increasing the alkali metal concentration (through high-pressure fabrication techniques), the transition temperature can be increased up to 5 K in C2Na (ref. 4). Superconductivity in C6Yb and C6Ca with and 11.5 K, respectively, and at ambient conditions has been observed. Here we explore the architecture of the states near the Fermi level and identify characteristics of the electronic band structure generic to GICs. In addition to the expected charge transfer from the intercalant atoms to the graphene sheets, resulting from the occupation of the π bands, we find that in all of those-and only those-compounds that superconduct, an interlayer state, which is well-separated from the carbon sheets, also becomes occupied. We show that the energy of the interlayer band is controlled by a combination of its occupancy and the separation between the carbon layers.