Glaucoma is a progressive eye disease that leads to optic nerve damage, causing irreversible vision loss if left untreated. Optical coherence tomography (OCT) has become a crucial tool for glaucoma diagnosis, offering high-resolution 3D scans of the retina and optic nerve. However, the conventional practice of condensing information from 3D OCT volumes into 2D reports often results in the loss of key structural details. To address this, we propose a novel hybrid deep learning model that integrates cross-attention mechanisms into a 3D convolutional neural network (CNN), enabling the extraction of critical features from the superior and inferior hemiretinas, as well as from the optic nerve head (ONH) and macula, within OCT volumes. We introduce Channel Attention REpresentations (CAREs) to visualize cross-attention outputs and leverage them for consistency-based multi-task fine-tuning, aligning them with Gradient-Weighted Class Activation Maps (Grad-CAMs) from the CNN's final convolutional layer to enhance performance, interpretability, and anatomical coherence. We have named this model AI-CNet3D (AI-`See'-Net3D) to reflect its design as an Anatomically-Informed Cross-attention Network operating on 3D data. By dividing the volume along two axes and applying cross-attention, our model enhances glaucoma classification by capturing asymmetries between the hemiretinal regions while integrating information from the optic nerve head and macula. We validate our approach on two large datasets, showing that it outperforms state-of-the-art attention and convolutional models across all key metrics. Finally, our model is computationally efficient, reducing the parameter count by one-hundred--fold compared to other attention mechanisms while maintaining high diagnostic performance and comparable GFLOPS.