Defining droughts based on a single variable/index (e.g., precipitation, soil moisture, or runoff) may not be sufficient for reliable risk assessment and decision-making. In this paper, a multivariate, multi-index drought-modeling approach is proposed using the concept of copulas. The proposed model, named Multivariate Standardized Drought Index (MSDI), probabilistically combines the Standardized Precipitation Index (SPI) and the Standardized Soil Moisture Index (SSI) for drought characterization. In other words, MSDI incorporates the meteorological and agricultural drought conditions for overall characterization of drought. In this study, the proposed MSDI is utilized to characterize the drought conditions over several Climate Divisions in California and North Carolina. The MSDI-based drought analyses are then compared with SPI and SSI. The results reveal that MSDI indicates the drought onset and termination based on the combination of SPI and SSI, with onset being dominated by SPI and drought persistence being more similar to SSI behavior. Overall, the proposed MSDI is shown to be a reasonable model for combining multiple indices probabilistically.