Neuroimaging plays a key role in understanding the structural and functional brain changes associated with Alzheimer’s disease (AD), especially in multimodal pattern recognition. However, single-modality approaches often fail to capture the complex nature of disease progression, while many multimodal methods suffer from high computational cost, overfitting, and limited interpretability. To address these challenges, we propose an explainable multimodal learning framework that integrates structural Magnetic Resonance Imaging (MRI) and functional Positron Emission Tomography (PET) data for accurate and transparent AD diagnosis. The proposed pipeline introduces Multimodal Optimized Diffeomorphic Anatomical Registration (MoDAR) for consistent cross-modality alignment. Feature extraction and fusion are performed using a Soft Progressive Attention–Enclosed Sparse Probabilistic Variational Autoencoder (SPA-SPVA), which learns compact and discriminative representations. For disease staging, we developed a Convolutional Masked Transformer (CoMFormer) that captures both local imaging biomarkers and global dependencies. Model parameters are optimized using a sine-chaotic Greylag Goose Optimization Algorithm (SC-GGOA) strategy to ensure stable convergence. Shapley Additive exPlanations (SHAP) are employed to provide interpretable insights into model decisions. Experimental results on the AD Neuroimaging Initiative (ADNI) dataset demonstrate an accuracy of 98.14%, outperforming recent methods. The framework is generalizable and can be extended to other multimodal biomedical data, highlighting its potential for real-world healthcare applications.