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 (Formula presented.), 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.