Gliomas are aggressive brain tumors that infiltrate surrounding tissue beyond the visible tumor margins observed on Magnetic Resonance Imaging (MRI). Predicting the spatial extent of this infiltration is essential for surgical planning and radiation therapy, yet existing deep learning approaches focus on segmenting the visible tumor rather than estimating infiltration risk in the surrounding tissue. This paper presents InfiltrNet, a novel dual-branch architecture that combines a convolutional neural network (CNN) encoder with a Swin Transformer encoder through cross-attention fusion modules to predict three-zone infiltration risk maps from multimodal MRI. A label generation strategy based on distance transforms is proposed to derive reproducible infiltration risk zones from standard Brain Tumor Segmentation (BraTS) annotations. InfiltrNet is trained with a combined Dice-CrossEntropy and boundary-aware loss augmented by auxiliary supervision heads at intermediate decoder levels. Extensive experiments on BraTS 2020 and BraTS 2025 demonstrate that InfiltrNet outperforms five established baselines. Explainability analysis using GradCAM++ and Occlusion sensitivity confirms that the model attends to clinically relevant peritumoral regions.