Halogen substitution, that is, bromine for iodine, in the series of topological Bi_nTeI (n = 1, 2, 3) materials was conducted in order to explore the impact of anion exchange on topological electronic structure. In this proof-of-concept study, we demonstrate the applicability of the modular view on crystal and electronic structures of new Bi₂TeBr and Bi₃TeBr compounds. Along with the isostructural telluroiodides, they constitute a family of layered structures that are stacked from two basic building modules, _∞ ²[Bi₂] and _∞ ²[BiTeX] (X = I, Br). We present solid-state synthesis, thermochemical studies, crystal growth, and crystal-structure elucidation of Bi₂TeBr [space group R3m (no. 166), a = 433.04(2) pm, c = 5081.6(3) pm] and Bi₃TeBr [space group R3m (no. 160), a = 437.68(3) pm, c = 3122.9(3) pm]. First-principles calculations establish the topological nature of Bi₂TeBr and Bi₃TeBr. General aspects of chemical bonding appear to be similar for Bi_nTeX (X = I, Br) with the same n, so that alternation of the global gap size upon substitution is insignificant. The complex topological inversion proceeds between the states of two distinct modules, _∞ ²[Bi₂] and _∞ ²[BiTeBr]; thus, the title compounds can be seen as heterostructures built via a modular principle. Furthermore, highly disordered as well as incommensurately modulated ternary phase(s) are documented near the Bi₂TeBr composition. Single-crystal X-ray diffraction experiments on BiTeBr and Bi₂TeI resolve some discrepancies in prior published work.