The crystal structures of Ba5CuIr3O12 and Ba16Cu3Ir10O39 have been determined using a combination of X-ray and neutron powder diffraction data. Considering their structures to be based on hcp stacks of Ba3O9 and Ba3CuO6 layers, Ba5CuIr3O12 has a 10-layer structure, space group P3c1 with a = 10.14055(2) Å and c = 21.65993(9) Å. Ba16Cu3Ir10O39 has a 16-layer structure, space group P321with a = 10.13442(2) Å and c = 35.0564(2) Å. Sequences of trigonal prismatic and octahedral transition metal sites run in chains parallel to z, with Ba cations located between the chains. The distribution of Ir and Cu cations in the octahedral and trigonal prismatic sites is disordered in both compounds. Cu cations are displaced from the centers of the trigonal prisms toward the rectangular faces. Both materials may also be regarded as commensurate composites of two substructures, sharing common unit cell parameters a and b but with different parameters c1 and c2, where the ratio c1/c2 is a rational fraction. The relative merits of the oxide layer model and the composite crystal model are discussed.