Analyzing the phenomenon of folded bands in photoemission spectra of solids, we have disclosed the coexistence of two different representations of two-dimensional (2D) Brillouin zones for occupied graphite- and intercalant-derived electronic states in a La-graphite intercalation compound. These two representations are characterized by separated 2D Fermi-surface areas, which are related to the graphene and intercalant layer, respectively. Each individual area shows symmetry properties of the respective layer. Our fundamental finding is of high importance for deeper understanding of quasi-two-dimensional electronic properties in layered structures.