Flood analysis of urban drainage systems plays a crucial role for flood risk management in urban areas. Rainfall characteristics, including the dependence between rainfall variables, have a significant influence on flood frequency. This paper considers the use of copulas to represent the probabilistic dependence structure between rainfall depth and duration in the synthetic rainfall generation process, and the Gumbel copula is fitted for the rainfall data in a case study of sewer networks. The probabilistic representation of rainfall uncertainty is combined with fuzzy representation of model parameters in a unified framework based on Dempster–Shafer theory of evidence. The Monte Carlo simulation method is used for uncertainty propagation to calculate the exceedance probabilities of flood quantities (depth and volume) of the case study sewer network. This study demonstrates the suitability of the Gumbel copula in simulating the dependence of rainfall depth and duration, and also shows that the unified framework can effectively integrate the copula-based probabilistic representation of random variables and fuzzy representation of model parameters for flood analysis.