We performed angle-resolved photoemission experiments on CaC6 and measured k(z)-dependent electronic structures to investigate the interlayer states. The results reveal a spherical interlayer Fermi surface centered at the Gamma point. We also find that the graphene-driven band possesses a weak k(z) dispersion. The overall electronic structure shows a peculiar single-graphene-layer periodicity in the k(z) direction although the CaC6 unit cell is supposed to contain three graphene layers. This suggests that the c-axis ordering of Ca has little effect on the electronic structure of CaC6. In addition to CaC6, we also studied the a low-temperature superconductor BaC6. For BaC6, the graphene-band Dirac-point energy is smaller than that of CaC6. Based on data from CaC6 and BaC6, we rule out the C-xy phonon mode as the origin of the superconductivity in CaC6, which strongly suggests interlayer-state-driven superconductivity