Mobility as a Service (MaaS) offers an integrated platform that combines various transport services into a single, on-demand service point. This integration involves multiple stakeholders at different levels, categorized into three main perspectives: users, Transportation Service Providers (TSPs), and government. Considering the benefits and objectives of all these categories is complex for modeling and optimization. Therefore, a comprehensive model is needed to represent cost and benefit analysis for each of these stakeholders. To address these complexities, we propose a bi-level mathematical model that optimizes their interactions within a multimodal urban transportation framework, with MaaS serving as an intermediary to facilitate these interactions. The upper-level model targets the reduction of travel and monetary costs for users while enhancing revenue for TSPs. Simultaneously, the lower-level model focuses on maximizing the profit for a MaaS provider and minimizing the costs associated with purchasing services from TSPs. Government incentives are incorporated in the two levels to promote reward emission reductions and service improvements. Analysis using the Sioux Falls network shows substantial benefits; specifically, the integration led to a 37.09% reduction in costs and a 3.57% reduction in emissions. Sensitivity analysis further shows that as demand increases, MaaS becomes significantly more cost-effective compared to traditional transportation systems, although the emissions reduction benefit of MaaS diminishes with higher demand.