Topological insulators (TIs) are semiconductors with protected electronic surface states that allow dissipation‐free transport. TIs are envisioned as ideal materials for spintronics and quantum computing. In Bi14Rh3I9, the first weak 3D TI, topology presumably arises from stacking of the intermetallic [(Bi4Rh)3I]2+ layers, which are predicted to be 2D TIs and to possess protected edge‐states, separated by topologically trivial [Bi2I8]2− octahedra chains. In the new layered salt Bi12Rh3Cu2I5, the same intermetallic layers are separated by planar, i.e., only one atom thick, [Cu2I4]2− anions. Density functional theory (DFT)‐based calculations show that the compound is a weak 3D TI, characterized by , and that the topological gap is generated by strong spin–orbit coupling (E g,calc. ∼ 10 meV). According to a bonding analysis, the copper cations prevent strong coupling between the TI layers. The calculated surface spectral function for a finite‐slab geometry shows distinct characteristics for the two terminations of the main crystal faces ⟨001⟩, viz., [(Bi4Rh)3I]2+ and [Cu2I4]2−. Photoelectron spectroscopy data confirm the calculated band structure. In situ four‐point probe measurements indicate a highly anisotropic bulk semiconductor (E g,exp. = 28 meV) with path‐independent metallic conductivity restricted to the surface as well as temperature‐independent conductivity below 60 K.