The simultaneous occurrence of various types of defects in bearings makes their diagnosis more challenging owing to the resultant complexity of the constituent parts of the acoustic emission (AE) signals. To address this issue, a new approach is proposed in this paper for the detection of multiple combined faults in bearings. The proposed methodology uses a deep neural network (DNN) architecture to effectively diagnose the combined defects. The DNN structure is based on the stacked denoising autoencoder non-mutually exclusive classifier (NMEC) method for combined modes. The NMEC-DNN is trained using data for a single fault and it classifies both single faults and multiple combined faults. The results of experiments conducted on AE data collected through an experimental test-bed demonstrate that the DNN achieves good classification performance with a maximum accuracy of 95%. The proposed method is compared with a multi-class classifier based on support vector machines (SVMs). The NMEC-DNN yields better diagnostic performance in comparison to the multi-class classifier based on SVM. The NMEC-DNN reduces the number of necessary data collections and improves the bearing fault diagnosis performance.