Supramolecular three-dimensional self-assembly of nonlamellar lipids with fragments of the protein immunoglobulin results in a bicontinuous cubic phase fragmented into nanoparticles with open water channels (cubosomes). The structure of the diamond-type cubic nanoparticles is characterized experimentally by freeze-fracture electron microscopy, and it is mathematically modeled with nodal surfaces emphasizing the fluid-like undulations of the cubosomic interfaces. Based on scaling-up and scaling-down approaches, we present stable and intermediate-kind nanoparticles resulting from the cubosomic growth. Our results reveal the smallest stable diamond-type cubosomic entity that can serve as a building block of more complex nanostructured fluid drug delivery vehicles of therapeutic proteins. The evidence presented for lipid-bilayer undulations in the surface region of the protein/lipid cubosomes could have important consequences for possible applications of these hierarchically organized porous nanoparticles.