A major remaining challenge in the superconducting cuprates is the unambiguous differentiation of the composition and electronic structure of the CuO2 layers and those of the intermediate layers. The large c axis for these materials permits employing soft x-ray (930.3 eV) standing wave (SW) excitation in photoemission that yields atomic layer-by-layer depth resolution of these properties. Applying SW photoemission to Bi2Sr2CaCu2O8+δ yields the depth distribution of atomic composition and the layer-resolved densities of states. We detect significant Ca presence in the SrO layers and oxygen bonding to three different cations. The layer-resolved valence electronic structure is found to be strongly influenced by the atomic supermodulation structure, as determined by comparison to density functional theory calculations, by Ca-Sr intermixing, and by correlation effects associated with the Cu 3d-3d Coulomb interaction, further clarifying the complex interactions in this prototypical cuprate. Measurements of this type for other quasi-two-dimensional materials with large c represent a promising future direction.