Synergistic drug combination is a promising solution to cancer treatment. Since the combinatorial space of drug combinations is too vast to be traversed through experiments, computational methods based on deep learning have shown huge potential in identifying novel synergistic drug combinations. Meanwhile, the feature construction of drugs has been viewed as a crucial task within drug synergy prediction. Recent studies shed light on the use of heterogeneous data, while most studies make independent use of relational data of drug-related biomedical interactions and structural data of drug molecule, thus ignoring the intrinsical association between the two perspectives. In this study, we propose a novel deep learning method termed HetBiSyn for drug combination synergy prediction. HetBiSyn innovatively models the drug-related interactions between biomedical entities and the structure of drug molecules into different heterogeneous graphs, and designs a self-supervised learning framework to obtain a unified drug embedding that simultaneously contains information from both perspectives. In details, two separate heterogeneous graph attention networks are adopted for the two types of graph, whose outputs are utilized to form a contrastive learning task for drug embedding that is enhanced by hard negative mining. We also obtain cell line features by exploiting gene expression profiles. Finally HetBiSyn uses a DNN with batch normalization to predict the synergy score of a combination of two drugs on a specific cell line. The experiment results show that our model outperforms other state-of-art DL and ML methods on the same synergy prediction task. The ablation study also demonstrates that our drug embeddings with bi-perspective information learned through the end-to-end process is significantly informative, which is eventually helpful to predict the synergy scores of drug combinations.