Key points: We present a unified framework, which combines knowledge graph embedding and multi-task learning, named KGE-UNIT, for joint prediction of DTIs and DDIs. KGE-UNIT enables simultaneous prediction of multiple types of molecular interactions and enhances the performance of each task, even when data availability is limited. Through KGE, KGE-UNIT can extract heterogeneous features from the drug knowledge graph to enhance the structural features of drug and protein nodes, which ultimately leads to an improvement in the quality of the features. Based on multi-task learning, in KGE-UNIT, a novel and effective encoder-decoder predictor (i.e., task-aware CNN-based encoder and task-aware attention decoder) is proposed to fuse better multimodal features, capture the contextual interactions of molecular tasks and enhance task awareness, leading to improved performance of all tasks. The results show that KGE-UNIT outperforms other state-of-art methods for both DTIs and DDIs prediction. Moreover, through the extension of PPIs prediction, the scalability of KGE-UNIT is demonstrated.