Recently, attention on herb-drug interactions has increased due to the extensive popularity of herbal products or dietary supplements. So far, herb-drug interactions mostly have been investigated through in-vivo/in-vitro experiments. However, the number of herb-drug interactions to test is dramatically increasing, and therefore the need for in-silico methods is rising to reduce the search space and costs. Here, we develop two machine-learning-based methods to investigate synergistic herb-drug interactions. In the first study, we develop a method based on the deep neural network to predict the Caco-2 monolayer permeability of chemical compounds, such as herbal compounds. We used all possible molecular descriptors as the input feature of our model and compared the overall performance with recently developed methods, which only used several molecular descriptors. We show that our approach has better prediction performance compared to previous studies. In the second study, we define new disease-specific features to predict synergistic compound combinations. We show that the newly defined disease-specific features allow us to investigate the synergism of various combinations of compounds, which could not be considered in previous studies. Lastly, by combining the two methods, we suggest novel herb-drug pairs that may express synergistic effect.