Recent advances in graph representation learning provide new opportunities for computational drug-target interaction (DTI) prediction. Inspired by the emerging graph mutual information-based algorithms, we propose MMIDTI, a multi-level mutual information-aware DTI prediction framework based on a heterogeneous network (i.e., drug-protein, drug-drug and protein-protein interaction network; drug-disease, drug-side-effect, and protein-disease association network; drug-structure and protein-sequence similarity network). More specifically, MMIDTI leverages an encoder-decoder framework that can learn the type-aware and meta-path augmented node representations by following a contrastive learning paradigm. The encoder part is a Graph Convolutional Network (GCN) and the decoder is an inner product of the learned representations to recover the original heterogeneous network. Meanwhile, MMIDTI exploits two levels of mutual information: (1) maximizing local mutual information, to obtain node representations that capture the global information content of the entire heterogeneous graph. (2) maximizing the global mutual information, to constrain the node representation to have desired statistical characteristics. Experimental results show that our model can achieve better prediction performance than state-of-the-art methods.