Droughts are pervasive hydrometeorological phenomena and global hazards, whose frequency and intensity are expected to increase in the context of climate change. Drought monitoring is of paramount relevance. Here we propose a hybrid model for drought detection that integrates both climatic indices and data-driven models in a hybrid deep learning approach. We exploit time-series of multi-scale Standardized Precipitation Evapotranspiration Index together with precipitation and temperature as inputs. We introduce a dual-branch recurrent neural network with convolutional lateral connections for blending the data. Experimental and ablative results show that the proposed system outperforms both the considered drought index and purely data-driven deep learning models. Our results suggest the potential of hybrid models for drought monitoring and open the door to synergistic systems that learn from data and domain knowledge altogether.