Traditional drug-target and drug-disease associations prediction tasks have been performed independently, without fully exploiting the relationships between drugs and various other entities, leading to inaccurate predictions. With the emergence of large-scale heterogeneous biological networks, multi-task learning can effectively enhance the accuracy of association prediction based on the associations between entities. In this study, we propose a multi-task learning framework named DTD-MTL to predict drug-target and drug-disease associations simultaneously. Firstly, it utilizes a multi-layer relational graph convolutional network (RGCN) to learn the features of each node in the drug-target-disease network. Subsequently, it obtains the initial feature of an edge by concatenating the features of the two nodes on the same edge. To coordinate different prediction tasks, drug features are shared among different tasks. Afterwards, the autoencoder (AE) is used to extract features from different types of edges. In order to make the learned edge features more suitable for different prediction tasks, the distance covariance (DC) is utilized to eliminate the specificity between different types of edges, thereby leveraging the relationships between different tasks more effectively. Finally, the drug-target and drug-disease associations predictions are achieved based on the edge features extracted by the AE. Experimental results on a widely-used dataset show that DTD-MTL outperforms the state-of-the-art methods in the prediction task of drug-target and drug-disease associations.