New ferroelectric layered materials were found in the pseudobinary system Bi5Nb3O15-ABi2Nb2O9 (A= Ba, Sr and Pb). Preliminary observations made by transmission electron microscopy indicate that these compounds exhibit a complex incommensurately modulated structure. A (3 + 1)D structural model is obtained using ab initio phasing by charge flipping based on the analysis of precession electron diffraction tomography data. The (3 + 1)D structure is further validated by a refinement against neutron powder diffraction. These materials possess a layered structure with discontinuous [Bi2O2] slabs and perovskite blocks. While these structural units are characteristics of Aurivillius phases, the existence of periodic crystallographic shear planes offers strong similarities with collapsed or stairlike structures known in high-Tc superconductors and related compounds. Using dielectric spectroscopy, we study the phase transitions of these new layered materials. For A = Ba and Sr, a Vögel-Fulcher-like behavior characteristic of the so-called relaxor ferroelectrics is observed and compared to "canonical" relaxors. For A = Sr, the absence of a Burns temperature separated from the freezing temperature appears as a rather unusual behavior.