To improve the appeal of carsharing, we propose an integrated operation scheme of carsharing and parking-sharing services, where a carsharing operator rents parking spaces from private owners to provide convenient parking options to carsharing users. We examine how the operator's profit and social welfare differ under the existing carsharing-only service scheme and a bundled carsharing and parking-sharing service scheme. In particular, multiple groups of decision makers, i.e., suppliers of shared parking spaces, platform operators, carsharing users and private vehicle users, and interactions among them are modeled in the context of an integrated sharing platform. The properties of carsharing user and private-vehicle traveler choice equilibrium are discussed. The profit-maximizing and social-optimal platform pricing and supply strategies are explored. Numerical examples illustrate that the bundled carsharing and parking-sharing service scheme holds the potential to improve the operator's profit and social welfare.