The search continues for nickel oxide-based materials with electronic properties similar to cuprate high-temperature superconductors1-10. The recent discovery of superconductivity in the doped infinite-layer nickelate NdNiO2 (refs. 11,12) has strengthened these efforts. Here, we use X-ray spectroscopy and density functional theory to show that the electronic structure of LaNiO2 and NdNiO2, while similar to the cuprates, includes significant distinctions. Unlike cuprates, the rareearth spacer layer in the infinite-layer nickelate supports a weakly interacting three-dimensional 5d metallic state, which hybridizes with a quasi-two-dimensional, strongly correlated state with 3dx2 y2 I symmetry in the NiO2 layers. Thus, the infinite-layer nickelate can be regarded as a sibling of the rare-earth intermetallics13-15, which are well known for heavy fermion behaviour, where the NiO2 correlated layers play an analogous role to the 4f states in rare-earth heavy fermion compounds. This Kondo- or Anderson-lattice-like `oxideintermetallic' replaces the Mott insulator as the reference state from which superconductivity emerges upon doping.