Caveolin is a monotopic integral membrane protein, widely expressed in metazoans and responsible for constructing enigmatic membrane invaginations known as caveolae. Recently, the high-resolution structure of a purified human caveolin assembly, the CAV1-8S complex, revealed a unique organization of 11 protomers arranged in a tightly packed, radially symmetric spiral disc. One face and the outer rim of this disc are hydrophobic, suggesting that the complex incorporates into membranes by displacing hundreds of lipids from one leaflet. The feasibility of this unique molecular architecture and its biophysical and functional consequences are currently unknown. Using Langmuir film balance measurements, we find that CAV1-8S is highly surface active, intercalating into lipid monolayers of various compositions. CAV1-8S can also incorporate into preformed bilayers, but only upon removal of phospholipids from the outer-facing leaflet. Atomistic and coarse-grained simulations of biomimetic bilayers support this "leaflet replacement" model and also reveal that CAV1-8S accumulates 40 to 70 cholesterol molecules into a disordered monolayer between the complex and its distal lipid leaflet. We find that CAV1-8S preferentially associates with positively curved membrane surfaces due to its influence on the conformations of distal leaflet lipids, and that these effects laterally sort lipids. Large-scale simulations of multiple caveolin assemblies confirmed their association with large, positively curved membrane morphologies consistent with the shape of caveolae. Further, association with curved membranes regulates the exposure of caveolin residues implicated in protein-protein interactions. Altogether, the unique structure of CAV1-8S imparts unusual modes of membrane interaction with implications for membrane organization, morphology, and physiology.