We hereby describe a strategy for obtaining novel topological nanostructures consisting of dual-cavity basket 1, forming a curved monolayer of large unilamellar vesicles in water (CAC < 0.25 μM), and bivalent guests 4/5 populating the cavities of such bolaamphiphilic hosts. On the basis of the results of (1)H NMR spectroscopy, electron microscopy, and dynamic light scattering measurements, we postulated that divalent guest molecules 4/5 cover the curved vesicular surface in a lateral fashion to satisfy the complexation [2 + 2] valency and thereby give stable two-dimensional supramolecular polymers [1⊂4]n and [1⊂5]n. The results of experimental studies are also supported with coarse-grained molecular dynamics simulations and molecular mechanics. Our discovery about the assembly of novel vesicular structures could be of interest for stabilization/functionalization of liposomal surfaces as well as detection of polyvalent molecules and removal of targeted substances from aqueous environments.