Halogen substitution, i. e. bromine for iodine, in the series of topological Bi n TeI (n = 1, 2, 3) materials is conducted in order to explore an impact of anion exchange on the topological electronic structure. In the proof-of-concept study we demonstrate the applicability of the modular view on the crystal and electronic structures of the new Bi 2 TeBr and Bi 3 TeBr compounds. Along with the isostructural telluroiodides, they constitute a family of layered structures that are stacked from two basic building modules, [ ஶ ଶ Bi 2 ] and [ ஶ ଶ BiTeX] (X = I, Br). We present solid-state synthesis, thermochemical studies, crystal growth and crystal-structure elucidation of Bi 2 TeBr (sp.gr. R3 തm (no. 166), a = 433.04(2) pm, c = 5081.6(3) pm) and Bi 3 TeBr (sp.gr. R3m (no. 160), a = 437.68(3) pm, c = 3122.9(3) pm). First-principles calculations establish the topological nature of Bi 2 TeBr and Bi 3 TeBr. General aspects of chemical bonding appear to be similar for Bi n TeX (X = I, Br) with the same n, so that the alternation of the global gap size upon substitution is insignificant. The complex topological inversion proceeds between the states of two distinct modules, [ ஶ ଶ Bi 2 ] and [ ஶ ଶ 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 Bi 2 TeBr composition. Single-crystal X-ray diffraction experiments on BiTeBr and Bi 2 TeI resolve some discrepancies in the prior published work.