Drug-drug interactions (DDIs) are a major cause of preventable hospitalizations and deaths. Recently, researchers in the AI community try to improve DDI prediction in two directions, incorporating multiple drug features to better model the pharmacodynamics and adopting multi-task learning to exploit associations among DDI types. However, these two directions are challenging to reconcile due to the sparse nature of the DDI labels which inflates the risk of overfitting of multi-task learning models when incorporating multiple drug features. In this paper, we propose a multi-task semi-supervised learning framework MLRDA for DDI prediction. MLRDA effectively exploits information that is beneficial for DDI prediction in unlabeled drug data by leveraging a novel unsupervised disentangling loss CuXCov. The CuXCov loss cooperates with the classification loss to disentangle the DDI prediction relevant part from the irrelevant part in a representation learnt by an autoencoder, which helps to ease the difficulty in mining useful information for DDI prediction in both labeled and unlabeled drug data. Moreover, MLRDA adopts a multi-task learning framework to exploit associations among DDI types. Experimental results on real-world datasets demonstrate that MLRDA significantly outperforms state-of-the-art DDI prediction methods by up to 10.3% in AUPR.