New three-dimensional (3D) topological phases can emerge in superlattices containing constituents of known two-dimensional topologies. Here we demonstrate that stoichiometric Bi1Te1, which is a natural superlattice of alternating two Bi2Te3 quintuple layers and one Bi bilayer, is a dual 3D topological insulator where a weak topological insulator phase and topological crystalline insulator phase appear simultaneously. By density functional theory, we find indices (0;001) and a non-zero mirror Chern number. We have synthesized Bi1Te1 by molecular beam epitaxy and found evidence for its topological crystalline and weak topological character by spin- and angle-resolved photoemission spectroscopy. The dual topology opens the possibility to gap the differently protected metallic surface states on different surfaces independently by breaking the respective symmetries, for example, by magnetic field on one surface and by strain on another surface.