Accurately predicting drug-target interaction (DTI) is a crucial step to drug discovery. Recently, deep learning techniques have been widely used for DTI prediction and achieved significant performance improvement. One challenge in building deep learning models for DTI prediction is how to appropriately represent drugs and targets. Target distance map and molecular graph are low dimensional and informative representations, which however have not been jointly used in DTI prediction. Another challenge is how to effectively model the mutual impact between drugs and targets. Though attention mechanism has been used to capture the one-way impact of targets on drugs or vice versa, the mutual impact between drugs and targets has not yet been explored, which is very important in predicting their interactions.;Therefore, in this article we propose MINN-DTI, a new model for DTI prediction. MINN-DTI combines an interacting-transformer module (called Interformer) with an improved Communicative Message Passing Neural Network (CMPNN) (called Inter-CMPNN) to better capture the two-way impact between drugs and targets, which are represented by molecular graph and distance map, respectively. The proposed method obtains better performance than the state-of-the-art methods on three benchmark datasets: DUD-E, human and BindingDB. MINN-DTI also provides good interpretability by assigning larger weights to the amino acids and atoms that contribute more to the interactions between drugs and targets.;The data and code of this study are available at https://github.com/admislf/MINN-DTI.