Climate change stresses the need for research and development of innovative sustainable mobility solutions that provide reliable and convenient door-to-door services for both passengers and freight. The increase in urban population and the popularity of e-commerce further highlights the need for action. In this regard, crowd-shipping is often perceived as an efficient, cost-effective, and sustainable alternative (or complement) to the management of urban freight mobility through efficient utilization of current transportation capacities. In this framework, inspired by the concept of MaaS (Mobility as a Service) in integrating various forms of transport and transport-related services into a single on-demand mobility service, this paper proposes a car-sharing-based service for the combined mobility of passengers and freight. In doing so, one-way car-sharing and crowd-shipping concepts are integrated in order to serve part of the existing freight demand in a sustainable and cost-efficient way for users, societies, and the environment. An optimization model is proposed to optimally plan the activation of one-way car-sharing and crowd-shipping services and to determine the optimal number of vehicles to assign to them. Such decisions are aimed at minimizing the total imbalance by serving passenger and freight demand during different time periods. In doing so, the willingness of users to carry freight in their vehicles is also taken into consideration. The capability of the proposed approach is evaluated through representative numerical examples aimed at showing the impact of the model parameters on the solution.