The fast-growing carsharing and ride-hailing businesses are generating economic benefits and societal impacts in modern society, while both have limitations to satisfy diverse users, e.g., travelers in low-income, underserved communities. In this article, we consider two types of users: Type 1 drivers who rent shared cars and Type 2 passengers who need shared rides. We propose an integrated car-and-ride sharing (CRS) system to enable community-based shared transportation. To compute solutions, we propose a two-phase approach where in Phase I we determine initial car allocation and Type 1 drivers to accept; in Phase II we solve a stochastic mixed-integer program to match the accepted Type 1 drivers with Type 2 users, and optimize their pick-up routes under a random travel time. The goal is to minimize the total travel cost plus expected penalty cost of users waiting and system overtime. We demonstrate the performance of a CRS system in Washtenaw County, Michigan by testing instances generated based on census data and different demand patterns. We also demonstrate the computational efficacy of our decomposition algorithm benchmarked with the traditional Benders decomposition for solving the stochastic model in Phase II. Our results show high demand fulfillment rates and effective matching and scheduling with low risk of waiting and overtime.