Probabilistic assessment of drought plays an important role in providing valuable information for evaluating water resources systems under drought conditions, and bivariate copulas are effective and efficient for the probabilistic assessment of drought based on joint distributions and/or joint return periods of drought characteristics. In this study, hydrological drought events and their characteristics (including duration and severity) in the Tien Yen River Basin of Quang Ninh province are detected using the Standardized Streamflow Index (SSFI). The BB8Copula is selected as the best-fit copula for hydrological drought duration and severity. Joint probabilities and joint return periods of drought duration and severity in the cases “and” and “or” are calculated based on the BB8Copula, which are employed for drought assessment. The results show that the drought events with 1-season or cross-quarter duration were more popular than others; joint probabilities and joint return periods of the detected drought events from 1962 to 2009, ranged from 0.2% to 92.2% and from 0.782 years to 315.414 years, respectively, in the case “and”, and ranged from 3.8% to 99.6% and from 0.724 years to 18.785 years, respectively, in the case “or”.