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Urban road facilities are typically shared by heterogeneous traffic, such as cars, buses, and bicycles. This paper investigates the car and bicycle traffic at the network level by extending the 3D-MFD model to the car-bicycle network. Statistical 3D-MFDs for the car-bicycle traffic are proposed and empirically estimated for three selected networks in Shanghai. Simulation-based 3D-MFDs are used to determine the network bicycle capacity and validate statistical 3D-MFDs. Estimation results quantify negative marginal effects of car and bicycle density on network car speeds, and confirm the negative effect of bi-modal speed difference on bicycle traffic. When looking into the predicted results of 3D-MFDs, the maximum bi-modal production changes with the accumulation of bicycles, indicating car-bicycle interactions within the network. Few empirical observations are in the optimum operation regime, which indicate the potential of improving the multi-modal networks. Findings of this study can benefit network designs and traffic operations, such as adjusting separation types, implementing stricter bicycle management, and extending bicycle priority in certain areas. [ABSTRACT FROM AUTHOR]