Palm vein biometric technology is widely regarded as highly secure due to its challenging-to-forge characteristics. However, recent empirical studies have revealed that forged vein patterns printed on paper can deceive palm vein recognition systems, thereby leading to security breaches. The conventional approach to address this issue involves performing liveness detection followed by preprocessing the palm vein image prior to recognition, which increases the algorithmic complexity and might adversely affect overall performance. To overcome these limitations, we propose a multibranch network (PVCodeNet++) for end-to-end integration of palm vein recognition and liveness detection using a multitask learning approach. Specifically, our proposed model leverages network weight sharing and mutual assistance between network branches to enhance overall performance. We utilize the transformer encoder as the underlying shared component, employ central difference convolution for the liveness detection branch, introduce the normalized attention mechanism, and balance the multitask loss through the uncertainty weighting method. Experiments on palm vein liveness and spoofing datasets show that the proposed PVCodeNet++ has an equal error rate of 0 for recognition performance metrics on various datasets, a significant improvement in the intraclass compactness and interclass separability separation metric, increasing from 7.88 to 9.37 on the PolyU dataset; and an average classification error rate of 0 for liveness detection performance metrics, demonstrating the feasibility and effectiveness of the method proposed.