Public transport (PT) agencies are increasingly keen on integrating ride-hailing (RH) services with PT to improve overall mobility. Understanding the traffic flow distribution in the integrated system is vital for the policy decision-making and services design of such a system. We propose a stochastic user equilibrium (SUE) model for multimodal transport systems consisting of private car, PT and RH. The travel costs in the SUE model are investigated using a multimodal graph representation to capture the relationship of different travel modes in the integrated system. We apply the proposed model to a toy case and a real-world case. A RH subsidy strategy is compared with the benchmark to demonstrate travellers’ route and mode shifts in the integrated system. Our findings offer insights on subsidising RH services through the proposed model, and provide valuable knowledge on the planning and design of the integrated system.