A detailed study of the structure-property relationship is reported for the first four members of the high-Tc superconducting homologous series of (Cu,Mo)Sr2(Ce,Y)sCu2O5+2s+δ [(Cu,Mo)−12s2]. In this series, the adjacent CuO2 planes are separated by a single Y-cation layer for s=1 and a fluorite-type (Ce,Y)−[O2−(Ce,Y)]s−1 layer block for s≥2. Even though this series may be considered a conventional homologous series from the chemical point of view, we emphasize that the structures are different from those of the Tl-, Hg-, Bi-, etc.,-based series by the fact that the inserted fluorite-type blocks are insulating. We show the formation of the higher s members via intercalation of additional Ce-O2 layer(s) into the crystal lattices of the lower members of the series. Neutron powder-diffraction data demonstrate that the Ce/Y ratio is not constant at the different (Ce,Y) layers in the fluorite-structured block and that the innermost (Ce,Y) layer(s) are significantly Ce rich compared with the outer ones. Two independent crystallographic sites are identified for the extra oxygen atoms in the basal (Cu0.75Mo0.25)O1+δ plane with site fractional occupancies that strongly correlate with the properties of the material. A short-range ordered structure is proposed for the (Cu0.75Mo0.25)O1+δ layers that could explain both the superconducting properties of the materials and the enhanced Tc for the first member of the series.