Major depressive disorder (MDD) is a prevalent mental disorder associated with complex neurobiological changes that cannot be fully captured using a single imaging modality. The use of multimodal magnetic resonance imaging (MRI) provides a more comprehensive understanding of brain changes by combining structural and functional data. Despite this, the effective integration of these modalities remains challenging. In this study, we propose a dual cross-attention-based multimodal fusion framework that explicitly models bidirectional interactions between structural MRI (sMRI) and resting-state functional MRI (rs-fMRI) representations. The proposed approach is tested on the large-scale REST-meta-MDD dataset using both structural and functional brain atlas configurations. Numerous experiments conducted under a 10-fold stratified cross-validation demonstrated that the proposed fusion algorithm achieves robust and competitive performance across all atlas types. The proposed method consistently outperforms conventional feature-level concatenation for functional atlases, while maintaining comparable performance for structural atlases. The most effective dual cross-attention multimodal model obtained 84.71% accuracy, 86.42% sensitivity, 82.89% specificity, 84.34% precision, and 85.37% F1-score. These findings emphasize the importance of explicitly modeling cross-modal interactions for multimodal neuroimaging-based MDD classification.