This work introduces a novel biorthogonal tunable wavelet unit constructed using a lifting scheme that relaxes both the orthogonality and equal filter length constraints, providing greater flexibility in filter design. The proposed unit enhances convolution, pooling, and downsampling operations, leading to improved image classification and anomaly detection in convolutional neural networks (CNN). When integrated into an 18-layer residual neural network (ResNet-18), the approach improved classification accuracy on CIFAR-10 by 2.12% and on the Describable Textures Dataset (DTD) by 9.73%, demonstrating its effectiveness in capturing fine-grained details. Similar improvements were observed in ResNet-34. For anomaly detection in the hazelnut category of the MVTec Anomaly Detection dataset, the proposed method achieved competitive and wellbalanced performance in both segmentation and detection tasks, outperforming existing approaches in terms of accuracy and robustness.