MRI is pivotal in diagnosing brain injuries in infants. However, the dynamic development of the brain introduces variability in infant MRI characteristics, posing challenges for MRI-based classification in this population. Furthermore, manual data selection in large-scale studies is labor-intensive, and existing algorithms often underperform with thick-slice MRI data. To enhance research efficiency and classification accuracy in large datasets, we propose an advanced classification model. We introduce the Dual-Branch Attention Information Interactive Neural Network (DBAII-Net), a cutting-edge model inspired by radiologists' use of multiple MRI sequences. DBAII-Net features two innovative modules: (1) the Convolutional Enhancement Module (CEM), which leverages advanced convolutional techniques to aggregate multi-scale features, significantly enhancing information representation; and (2) the Cross-Modal Attention Module (CMAM), which employs state-of-the-art attention mechanisms to fuse data across branches, dramatically improving positional and channel feature extraction. Performances (accuracy, sensitivity, specificity, area under the curve, etc.) of DBAII-Net were compared with eight benchmark models for brain MRI classification in infants aged 6 months to 2 years. Utilizing a self-constructed dataset of 240 thick-slice brain MRI scans (122 with brain injuries, 118 without), DBAII-Net demonstrated superior performance. On a test set of approximately 50 cases, DBAII-Net achieved average performance metrics of 92.53% accuracy, 90.20% sensitivity, 94.93% specificity, and an area under the curve (AUC) of 0.9603. Ablation studies confirmed the effectiveness of CEM and CMAM, with CMAM significantly boosting classification metrics. DBAII-Net with CEM and CMAM outperforms existing benchmarks in enhancing the precision of brain MRI classification in infants, significantly reducing manual effort in infant brain research. Our code is available at https://github.com/jiazhen4585/DBAII-Net.