Mild Traumatic Brain Injury (mTBI) is a significant public health challenge due to its high prevalence and potential for long-term health effects. Despite Computed Tomography (CT) being the standard diagnostic tool for mTBI, it often yields normal results in mTBI patients despite symptomatic evidence. This fact underscores the complexity of accurate diagnosis. In this study, we introduce an interpretable 3D Multi-Modal Residual Convolutional Neural Network (MRCNN) for mTBI diagnostic model enhanced with Occlusion Sensitivity Maps (OSM). Our MRCNN model exhibits promising performance in mTBI diagnosis, demonstrating an average accuracy of 82.4%, sensitivity of 82.6%, and specificity of 81.6%, as validated by a five-fold cross-validation process. Notably, in comparison to the CT-based Residual Convolutional Neural Network (RCNN) model, the MRCNN shows an improvement of 4.4% in specificity and 9.0% in accuracy. We show that the OSM offers superior data-driven insights into CT images compared to the Grad-CAM approach. These results highlight the efficacy of the proposed multi-modal model in enhancing the diagnostic precision of mTBI.