This paper studies a real-time parking-sharing program with which owners of private parking spaces can lend out their parking spaces to other drivers to park when these are not in use. Compared with curbside and garage parking problems, the information of supplies and demands is randomly announced by drivers and owners respectively via a parking-sharing APP installed on their smartphones. Besides, the parking spaces made available by independent owners are usually heterogeneous in terms of their locations and available time intervals. Thus, two critical issues need to be resolved: (a) appropriately matching demands and supplies under an uncertain setting; and (b) efficiently scheduling the demands matched to avoid potential parking conflicts. We propose a novel real-time reservation approach based on a rolling-horizon framework, which can assign multiple drivers to a single parking space in order to better utilize scarce parking resources. For each period, an integrated optimal matching-and-scheduling problem is formulated as a mixed integer programming model and proved to be strongly NP-hard. To fast generate a near-optimal solution to the problem, a two-stage heuristics derived from the minimum-cost flow problem is developed. The computational results validate the efficiency and effectiveness of the proposed approach. Some operational insights are also presented and discussed.