Modeling the interactions between drugs, targets, and diseases is paramount in drug discovery and has significant implications for precision medicine and personalized treatments. Current approaches frequently consider drug-target or drug-disease interactions individually, ignoring the interdependencies among all three entities. Within human metabolic systems, drugs interact with protein targets in cells, influencing target activities and subsequently impacting biological pathways to promote healthy functions and treat diseases. Moving beyond binary relationships and exploring tighter triple relationships is essential to understanding drugs' mechanism of action (MoAs). Moreover, identifying the heterogeneity of drugs, targets, and diseases, along with their distinct characteristics, is critical to model these complex interactions appropriately. To address these challenges, we effectively model the interconnectedness of all entities in a heterogeneous graph and develop a novel Heterogeneous Graph Triplet Attention Network (\texttt{HeTriNet}). \texttt{HeTriNet} introduces a novel triplet attention mechanism within this heterogeneous graph structure. Beyond pairwise attention as the importance of an entity for the other one, we define triplet attention to model the importance of pairs for entities in the drug-target-disease triplet prediction problem. Experimental results on real-world datasets show that \texttt{HeTriNet} outperforms several baselines, demonstrating its remarkable proficiency in uncovering novel drug-target-disease relationships.