The electronic structure of coaxial, graphene double‐layer tubules is predicted for various combinations of metallic and insulating constituent inner and outer monolayers, depending on the diameter and chirality of the tubule. For the examples chosen, some of the energy bands of the inner and outer tubules are coupled to each other by commensurate interlayer interactions. Nevertheless, because of symmetry, the energy bands of metallic monolayer tubules remain metallic even after interlayer interactions are considered. The possible implications of these results on molecular metal‐insulator devices are discussed.