We reveal the existence of a general class of supramolecular assemblies made up of lipid-coated polyelectrolytes including the celebrated lipid nucleic acid complexes. With the aid of high-resolution cryo-electron microscopy, we unveil the nanoscale internal organization of assemblies generated with a wide range of synthetic and biological polyelectrolytes, several of them being investigated in this context for the first time, namely, poly(styrene sulfonic acid), carboxylmethylcellulose, and filamentous actin. Using an original coarse-grained model representing lipid-coated polyelectrolytes as semiflexible tubes, we thoroughly explored the morphologies resulting from the self-assembly process as a function of tube lengths and rigidities; the computed structures are fully consistent with the experimental observations. In particular, we found a strong extension of the correlation range of the order parameter as the rigidity of the lipid-coated polyelectrolytes increases. Electrostatic interactions provide a stabilizing mechanism leading to finite-size equilibrium assemblies. These assemblies may constitute a generic route for interfacing polyelectrolytes to living cells to perform gene delivery, for instance.