Sudden metro service interruptions can result in train delays and passenger congestion at stations. This, in turn, will present significant challenges for passenger evacuation and emergency management. To evaluate the performance of urban public transport networks under such disruptions, this paper proposes a composite network resilience assessment method based on resilience theory, which considers passengers’ multi-path decision-making for travel in the event of sudden disruptions. Firstly, the construction of an urban public transport composite network model, which considers the “one-to-many” coupling mode of stations, is based on the combination of passenger flow and geographic information data. This model is used to determine the network interruption intervals under different faulty stations. Secondly, the inter-layer traffic distribution of the network is carried out, taking into account the passengers’ multi-path decision-making in emergencies and calculating their travel times. Ultimately, an evaluation framework for the resilience of the composite network is established based on the composite network performance function. Furthermore, the network resilience levels under disparate interruption scenarios are contrasted through case analysis. The findings indicate that there are notable discrepancies in the network resilience levels under varying station failures. Among these discrepancies, the interruption interval of the network, the passenger flow volume of the lines, and the conditions of the subway-coupled bus stations will all influence the network resilience under interruptions. The resilience assessment method for urban bus composite networks proposed in this study can serve as a reference for the development of emergency response plans in the event of sudden disruptions.