Mobility-as-a-Service (MaaS) is an emerging business model integrating various travel modes into a single mobility service accessible on demand. Besides the on-demand mobility services, instant delivery services have increased rapidly and particularly boomed during the coronavirus (COVID-19) pandemic, requiring online orders to be delivered timely. In this study, to deal with the redundant mobility resources and high costs of instant delivery services, we model an MaaS ecosystem that provides mobility and instant delivery services by sharing the same multimodal transport system. We derive a two-class bundle choice user equilibrium (BUE) for mobility and delivery users in the MaaS ecosystems. We propose a bilateral surcharge–reward scheme (BSRS) to manage the integrated mobility and delivery demand in different incentive scenarios. We further formulate a bilevel programming problem to optimize the proposed BSRS, where the upper level problem aims to minimize the total system equilibrium costs of mobility and delivery users, and the lower level problem is the derived two-class BUE with BSRS. We analyze the optimal operational strategies of the BSRS and develop a solution algorithm for the proposed bilevel programming problem based on the system performance under BSRS. Numerical studies conducted with real-world data validate the theoretical analysis, highlight the computational efficiency of the proposed algorithm, and indicate the benefits of the BSRS in managing the integrated mobility and delivery demand and reducing total system equilibrium costs of the MaaS ecosystems.