AgBi₂S₂Cl₃ and three members of the Ag_2xBi_4-2xS_6-4xBr_4x solid solution (x = 0.50 (I), x = 0.64 (II), and x = 0.73 (III)) were synthesized from Bi ₂S₃, AgX and BiSX (X = Cl, Br) at 720 K. X-ray diffraction on single crystals revealed that the compounds crystallize in the monoclinic space groups C2/m (No. 12) with a = 1257.3(3), b = 400.0(1), c = 804.1(2) pm, β = 111.0(1)° for AgBi₂S₂Cl₃, a = 1331.3(5), b = 408.0(2), c = 972.0(3) pm, β = 90.8(1)° for (I), a = 1328.9(4), b = 408.5(1), c = 973.4(4) pm, β = 90.9(1)° for (II), and a = 1332.4(3), b = 409.3(1), c = 974.3(2) pm, β = 90.4(1)° for (III). AgBi₂S₂Cl₃ adopts a variant of the InBi ₂S₄Cl structure type, the isostructural compounds (I), (II) and (III) are related to the orthorhombic FeUS₃ type. All four compounds belong to homologous series with general formula [BiSA] ₂·[Ag_xBi_1-xS_2-2xX _2x-1]_N+1 (X = Cl, Br), which resemble minerals of the pavonite series. They are characterized by the parameters N and x and are denoted ^{(N, x)}P. In the crystal structures, two kinds of layered modules, A and B, alternate. Modules of type B are composed of chains of edge-sharing [MBr₄Z₂] octahedra (M = Ag/Bi; X = Cl, Br; Z = S/X) and vary in thickness N. Modules of type A uniformly consist of rows of paired monocapped trigonal prisms around Bi atoms with [MS₄Z ₂] octahedra around mixed-occupied metal positions (M = Ag/Bi) between them. Ag-Bi₂S₂Cl₃ comprises modules of type A only (N = 0) and is the silver-rich end-member (x = 1) in the series ^{(0, x)}P. (I) to (III) belong to the ^{(1, x)}P series with B modules of thickness N = 1. Calculations of the electronic band structures indicate that the compounds should act as indirect semiconductors with band gaps between 1.5 and 0.6 eV.