A method of liposome-based therapy for a mammalian subject is disclosed. The method uses liposomes with outer surfaces that contain an affinity moiety effective to bind specifically to a biological surface at which the therapy is aimed, and a hydrophilic polymer coating effective to shield the affinity moiety from interaction with the target surface. The hydrophilic polymer coating is made up of polymer chains covalently linked to surface lipid components in the liposomes through releasable linkages. After a desired liposome biodistribution is achieved, a releasing agent is administered to cause cleaving of a substantial portion of the releasable linkages in the liposomes, to expose the affinity agent to the target surface.