This study introduces an approach to copula model parameter estimation within a Bayesian framework. The model is applied to estimate the return periods of the 2013–2015 drought in the Han River watershed (South Korea) as observed through a network of 18 rainfall stations in the watershed. For the univariate return periods, some of the 2013–2015 drought durations (i.e., 9–24 months) have return periods of around 30 years while the drought severities (which range from about 400 to 1,400 mm) at certain stations might be regarded as extreme events with return periods in the hundreds of years. The recent drought is extraordinary at many stations in the Han River watershed although the associated uncertainty is quite large (e.g., for the Seoul station, a range of about 180 to 2,250 years). Moreover, it is clearly seen that the unprecedented joint return periods of the 2013–2015 drought at many stations are consistent with the very high drought severity. The joint return period of the drought duration and severity is above 100 years for many of the stations and upwards of 1,000 years for a few stations.