The n = 3-6 members of a new perovskite-based homologous series Bi3n+1Ti7Fe3n-3O9n+11 are reported. The crystal structure of the n = 3 Bi10Ti7Fe6O38 member is refined using a combination of X-ray and neutron powder diffraction data (a = 11.8511(2) Å, b = 3.85076(4) Å, c = 33.0722(6) Å, S.G. Immm), unveiling the partially ordered distribution of Ti4+ and Fe3+ cations and indicating the presence of static random displacements of the Bi and O atoms. All Bi3n+1Ti7Fe3n-3O9n+11 structures are composed of perovskite blocks separated by translational interfaces parallel to the (001)p perovskite planes. The thickness of the perovskite blocks increases with n, while the atomic arrangement at the interfaces remains the same. The interfaces comprise chains of double edge-sharing (Fe,Ti)O6 octahedra connected to the octahedra of the perovskite blocks by sharing edges and corners. This configuration shifts the adjacent perovskite blocks relative to each other over a vector 1/2p and creates S-shaped tunnels along the  direction. The tunnels accommodate double columns of the Bi3+ cations, which stabilize the interfaces owing to the stereochemical activity of their lone electron pairs. The Bi3n+1Ti7Fe3n-3O9n+11 structures can be formally considered either as intergrowths of perovskite modules and polysynthetically twinned modules of the Bi2Ti4O11 structure or as intergrowths of the 2D perovskite and 1D anatase fragments. Transmission electron microscopy (TEM) on Bi10Ti7Fe6O38 reveals that static atomic displacements of Bi and O inside the perovskite blocks are not completely random; they are cooperative, yet only short-range ordered. According to TEM, the interfaces can be laterally shifted with respect to each other over ±1/3a, introducing an additional degree of disorder. Bi10Ti7Fe6O38 is paramagnetic in the 1.5-1000 K temperature range due to dilution of the magnetic Fe3+ cations with nonmagnetic Ti4+. The n = 3, 4 compounds demonstrate a high dielectric constant of 70-165 at room temperature.