A novel cubic bicontinuous morphology is found in polymer-ceramic nanocomposites and mesoporous alum inosilicates that are derived by an amphiphilic diblock copolymer, poly(isoprene-b-ethylene oxide) (PI-b-PEO), used as a structure-directing agent for an inorganic aluminosilicate. Small-angle X-ray scattering (SAXS) was employed to unambiguously identify the Im3m crystallographic symmetry of the materials by fitting individual Bragg peak positions in the two-dimensional X-ray images. Structure factor calculations, in conjunction with results from transmission electron microscopy, were used to narrow the range of possible structures consistent with the symmetry and showed the plumber's nightmare morphology to be consistent with the data. The samples are made by deposition onto a substrate that imposes a strain field, generating a lattice distortion. This distortion is quantitatively analyzed and shown to have resulted in shrinkage of the crystallites by approximately one-third in a direction perpendicular to the substrate, in both as-made composites and calcined ceramic materials. Finally, the observation of the bicontinuous block-copolymer-derived hybrid morphology is discussed in the context of a pseudo-ternary morphology diagram and compared to existing studies of ternary phase diagrams of amphiphiles in a mixture of two solvents. The calcined mesoporous materials have potential applications in the fields of catalysis, separation technology, and microelectronics.