Urban road networks are frequently disrupted by flooding rainfall-flood disasters, which can cause severe traffic disruptions and leading to traffic congestion due to cascading effect. This paper investigates the reliability issues under rainfall-flood conditions. A coupled model, integrating a rainfall-flood model with an improved cascading failure model, is proposed to assess how rainfall intensities and flooding will influence traffic congestion and bring network instability. Utilizing an improved Nonlinear Load-Capacity model, we quantify the impact of congestion and analyze cascading processes under various rainfall-flood conditions. The case study in Nanjing, China reveal that, when congestion causes network pressure to exceed the traffic percolation threshold, traffic congestion diffusion becomes more pronounced, putting excessive strain on other passable roads. Network cascading failures due to traffic congestion diffusion can lead to excessive focus on the remaining passable roads, resulting in a sharp increase in the average importance. The significance of this work lies in its provision of an effective method for predicting potential network disruptions and cascading failures in advance, thereby enhancing post-disaster road operations.