MOTIVATION: Identifying the relationships among long non-coding RNAs (lncRNAs), microRNAs (miRNAs) and diseases is highly valuable for diagnosing, preventing, treating and prognosing diseases. The development of effective computational prediction methods can reduce experimental costs. While numerous methods have been proposed, they often to treat the prediction of lncRNA-disease associations (LDAs), miRNA-disease associations (MDAs) and lncRNA-miRNA interactions (LMIs) as separate task. Models capable of predicting all three relationships simultaneously remain relatively scarce. Our aim is to perform multi-task predictions, which not only construct a unified framework, but also facilitate mutual complementarity of information among lncRNAs, miRNAs and diseases. RESULTS: In this work, we propose a novel unsupervised embedding method called graph contrastive learning for multi-task prediction (GCLMTP). Our approach aims to predict LDAs, MDAs and LMIs by simultaneously extracting embedding representations of lncRNAs, miRNAs and diseases. To achieve this, we first construct a triple-layer lncRNA-miRNA-disease heterogeneous graph (LMDHG) that integrates the complex relationships between these entities based on their similarities and correlations. Next, we employ an unsupervised embedding model based on graph contrastive learning to extract potential topological feature of lncRNAs, miRNAs and diseases from the LMDHG. The graph contrastive learning leverages graph convolutional network architectures to maximize the mutual information between patch representations and corresponding high-level summaries of the LMDHG. Subsequently, for the three prediction tasks, multiple classifiers are explored to predict LDA, MDA and LMI scores. Comprehensive experiments are conducted on two datasets (from older and newer versions of the database, respectively). The results show that GCLMTP outperforms other state-of-the-art methods for the disease-related lncRNA and miRNA prediction tasks. Additionally, case studies on two datasets further demonstrate the ability of GCLMTP to accurately discover new associations. To ensure reproducibility of this work, we have made the datasets and source code publicly available at https://github.com/sheng-n/GCLMTP.