Growing evidence from recent studies implies that microRNAs or miRNAs could serve as biomarkers in various complex human diseases. Since wet-lab experiments for detecting miRNAs associated with a disease are expensive and time-consuming, machine learning techniques for miRNA-disease association prediction have attracted much attention in recent years. A big challenge in building reliable machine learning models is that of data scarcity. In particular, existing approaches trained on the available small datasets, even when combined with precalculated handcrafted input features, often suffer from bad generalization and data leakage problems. We overcome the limitations of existing works by proposing a novel multitask graph convolution-based approach, which we refer to as MuCoMiD. MuCoMiD allows automatic feature extraction while incorporating knowledge from five heterogeneous biological information sources (associations between miRNAs/diseases and protein-coding genes (PCGs), interactions between protein-coding genes, miRNA family information, and disease ontology) in a multitask setting which is a novel perspective and has not been studied before. To effectively test the generalization capability of our model, we conduct large-scale experiments on the standard benchmark datasets as well as on our proposed large independent testing sets and case studies. MuCoMiD obtains significantly higher Average Precision (AP) scores than all benchmarked models on three large independent testing sets, especially those with many new miRNAs, as well as in the detection of false positives. Thanks to its capability of learning directly from raw input information, MuCoMiD is easier to maintain and update than handcrafted feature-based methods, which would require recomputation of features every time there is a change in the original information sources (e.g., disease ontology, miRNA/disease-PCG associations, etc.). We share our code for reproducibility and future research at https://git.l3s.uni-hannover.de/dong/cmtt.