Novel anion-deficient perovskite-based ferrites Pb2Ba2BiFe5O13 and Pb1.5Ba2.5Bi2Fe6O16 were synthesized by solid-state reaction in air. Pb2Ba2BiFe5O13 and Pb1.5Ba2.5Bi2Fe6O16 belong to the perovskite-based A(n)B(n)O(3n-2) homologous series with n = 5 and 6, respectively, with a unit cell related to the perovskite subcell a(p) as a(p)root 2 x a(p) x na(p) root 2. Their structures are derived from the perovsldte one by slicing it with 1/2[110](p)((1) over bar 01)(p) crystallographic shear (CS) planes. The CS operation results in ((1) over bar 01)(p)-shaped perovsldte blocks with a thickness of (n - 2) FeO6 octahedra connected to each other through double chains of edge-sharing FeO5 distorted tetragonal pyramids which can adopt two distinct mirror-related configurations. Ordering of chains with a different configuration provides an extra level of structure complexity. Above T approximate to 750 K for Pb2Ba2BiFe5O13 and T approximate to 400 K for Pb1.5Ba2.5Bi2Fe6O16 the chains have a disordered arrangement. On cooling, a second-order structural phase transition to the ordered state occurs in both compounds. Symmetry changes upon phase transition are analyzed using a combination of superspace crystallography and group theory approach. Correlations between the chain ordering pattern and octahedral tilting in the perovskite blocks are discussed. Pb2Ba2BiFe5O13 and Pb1.5Ba2.5Bi2Fe6O16 undergo a transition into an antiferromagnetically (AFM) ordered state, which is characterized by a G-type AFM ordering of the Fe magnetic moments within the perovsldte blocks. The AFM perovsldte blocks are stacked along the CS planes producing alternating FM and AFM-aligned Fe-Fe pairs. In spite of the apparent frustration of the magnetic coupling between the perovskite blocks, all n = 4, 5, 6 A(n)Fe(n)O3(n-2) (A = Pb, Bi, Ba) feature robust antiferromagnetism with similar Neel temperatures of 623-632 K.