Drawing on complex network theory, this paper combines bus network and subway network into a multi-subnet composited complex network (MSCCN) of urban public transport (UPT). Then, the cascading failure of the MSCCN nodes and edges was modelled, and the passenger flow transfer rules were established under node and edge failures. Considering the impact of extreme weather on the UPT, a synthetic operator was created to measure the robustness of UPT MSCCN, in the light of network topology and passenger flow, and used to quantify the robustness of UPT MSCCN under extreme weather. Finally, a UPT MSCCN was set up for Qingdao, China, and subject to cascading failure simulation. The simulation results reveal how MSCCN robustness changes with different variables. The research findings help to optimize the response of the MSCCN to extreme weather.