Urban public transportation often exhibits pronounced spatio-temporal imbalances in passenger demand, resulting in capacity shortages during peak periods and excessive idle capacity during off-peak times. Meanwhile, with the expansion of e-commerce, urban freight demand continues to grow, making the use of idle public transportation space for freight transport an ideal approach. This study proposes an optimization framework for integrated passenger-freight co-transportation using Modular Autonomous Vehicles (MAVs), formulating a Mixed-Integer Quadratically Constrained Programming (MIQCP) Path-based model based on a space-time network to address the Modular Autonomous Unit (MAU) Routing Problem. The model integrates Fixed-Route Transit (FRT) and Demand-Responsive Transit (DRT), allowing MAUs to dynamically couple/decouple across different routes to meet the spatio-temporal demands of passengers and freight, with the objective of minimizing total operational costs. To tackle the computational complexity of large-scale instances, a customized Adaptive Large Neighborhood Search (ALNS) algorithm is designed, incorporating two initial solution generation methods (GUROBI and Greedy heuristic) and iteratively optimizing solutions through destroy and repair operations. A real-world case study based on the Shanghai bus network validates the effectiveness of the proposed approach. The results demonstrate that the MAU co-transportation system can effectively utilize vehicle compartment space to simultaneously transport passengers and freight, significantly reducing empty load rates, leading to a substantial reduction in operating costs. Without using the co-transportation mode, the number of MAUs used would increase significantly, accompanied by a 3.9% cost increase. Compared to the traditional combination of public transit and delivery vans, costs are reduced by 83.4%. This co-transportation modular transit system, with its unique flexibility, can provide efficient and low-cost transportation services for both passengers and freight within cities.