Analyzing and interpreting cone-beam computed tomography (CBCT) images is a complicated and often time-consuming process. In this study, we present two different architectures of multi-channel deep learning (DL) models: "Ensemble" and "Synchronized multi-channel", to automatically identify and classify skeletal malocclusions from 3D CBCT craniofacial images. These multi-channel models combine three individual single-channel base models using a voting scheme and a two-step learning process, respectively, to simultaneously extract and learn a visual representation from three different directional views of 2D images generated from a single 3D CBCT image. We also employ a visualization method called "Class-selective Relevance Mapping" (CRM) to explain the learned behavior of our DL models by localizing and highlighting a discriminative area within an input image. Our multi-channel models achieve significantly better performance overall (accuracy exceeding 93%), compared to single-channel DL models that only take one specific directional view of 2D projected image as an input. In addition, CRM visually demonstrates that a DL model based on the sagittal-left view of 2D images outperforms those based on other directional 2D images.Clinical Relevance- the proposed method aims at assisting orthodontist to determine the best treatment path for the patient be it orthodontic or surgical treatment or a combination of both.