The paper presents the development of a hybrid neural network architecture, BAFUNet, designed for the segmentation of spine MR images in the context of medical diagnostics. The architecture builds upon the classical U-Net, integrating atrous spatial pyramid pooling module in the bottleneck and a two-round fusion module in the skip connections to address challenges such as various object scales and unclear boundaries in medical images. The work describes the design of the proposed BAFUNet architecture, its implementation, and the experimental results. A comparative analysis was performed against classical U-Net and ResUNet++, demonstrating the relationship between the proposed architectural enhancements and segmentation performance. The evaluation was carried out using Dice score and Jaccard score metrics on the SPIDER dataset, a publicly available lumbar spine magnetic resonance imaging dataset. The results indicate that the BAFUNet architecture achieves a slight but consistent improvement in segmentation performance, with an average Dice Score increase of 0.003–0.005 compared to baseline models, highlighting its potential applicability in automated medical diagnostics.