We demonstrate the self-organization of quasi-one-dimensional nanostructures with periodic features using nature's primary three building blocks: lipids, DNA, and proteins. The periodicity of these "BioNanoStacks" is controllable through selection of the length of the DNA spacers. We show that BioNanoStacks can be reversibly assembled and disassembled through thermal melting of the DNA duplex, where the melting transition temperature is controllable not just by the DNA sequence and salt concentration, but also by the lipid composition within these superstructures. These novel materials may find applications in fields such as templated nanomaterial assembly, tissue-engineering scaffolds, or therapeutic delivery systems. Well-established techniques for chemical modification of biomolecules will also provide a broad platform for adaption and remodeling of these structures to provide optimal features for the required application.