Three-dimensional magnetic resonance images (MRI) have emerged as a valuable tool to diagnose and characterise Alzheimer's Disease (AD). Most current MRI analysis pipelines for AD detection focus on a single plane, limiting their ability to capture subtle changes associated with different stages of the disease. This paper proposes a novel deep learning-based pipeline called CoMRIAD that combines the three MRI planes (coronal, axial and sagittal, and referred to as combiplane) for enhanced AD detection and classification. Transfer learning architectures like InceptionV3, InceptionResNetV2, Xception, DenseNet121, and CNN were separately trained and tested on individual planes as well as the combiplane. Experimental results demonstrate that CoMRIAD outperforms single-plane MRI analysis, achieving a 6-8% increase in overall accuracy for two-way and four-way classification tasks. The heatmaps generated using GradCAM and Pearson's correlation coefficient computed between the original MRI and heatmap show high affinity to the predicted class. The CoMRIAD enhances AD detection from 3D MRI, facilitating the monitoring of the disease and relevant interventions. The source code CoMRIAD implementation can be found at: https://github.com/brai-acslab/comriad.