Amphiphilic block copolymers are molecules composed of hydrophilic and hydrophobic segments having the capacity to spontaneously self-assemble into a variety of supramolecular structures like micelles and vesicles. Here, we propose an original way to self-assemble amphiphilic block copolymers into a supported bilayer membrane for defined coating of nanoparticles. The heart of the method rests on a change of the amphiphilicity of the copolymer that can be turned off and on by varying the polarity of the solvent. In this condition, the assembly process can take advantage of specific molecular interactions in both organic solvent and water. While the concept potentially could be applied to any type of charged substrates, we focus our interest on the design of a new type of polymer assemblies mimicking the virus morphology. Namely, a capsid-like shell of glycoprotein-mimic amphiphilic block copolymer was self-assembled around a positively charged complex of RNA and polyethyleneimine. The process requires two steps. Block copolymers first interact with the complexes dispersed in DMSO through electrostatic interactions. Then, the increase of the water content in the medium triggers the hydrophobic effect and the concomitant self-assembly of free block copolymer molecules into a bilayer membrane at the complex surface. The higher gene silencing activity of the copolymer-modified complexes over the complexes alone shows the potential of this new type of nanoconstructs for biological applications, especially for the delivery of therapeutic biomolecules.