Cellular adhesion is an intricate physical process controlled by ligand-receptor affinity, density, mobility, and external forces transmitted through the elastic properties of the cell. As a model for cellular adhesion we study the detachment of cell-sized liposomes and membrane-coated silica beads from supported bilayers using atomic force microscopy. Adhesion between the two surfaces is mediated by the interaction between the adhesive lipid anchored saccharides lactosylceramide and the ganglioside GM3. We found that force-distance curves of liposome detachment have a very peculiar, partially concave shape, reminiscent of the nonlinear extension of polymers. By contrast, detachment of membrane coated beads led to force-distance curves similar to the detachment of living cells. Theoretical modelling of the enforced detachment suggests that the non-convex force curve shape arises from the mobility of ligands provoking a switch of shapes from spherical to unduloidal during detachment.