Chromosome identification is fundamental to karyotype analysis and underpins the diagnosis of genetic disorders and advances in biomedical research. However, the development of universally robust classification models is impeded by substantial inter-class morphological similarity, pronounced intra-class variability, and distributional shifts across multi-center datasets. In this study, we propose a novel multi-task deep learning framework that unifies supervised contrastive learning with explicit chromosome morphological reconstruction. Our approach jointly learns highly discriminative representations for classification and generates high-fidelity G-band patterns, thereby markedly improving morphological interpretability. We train the proposed model on over two million chromosome images collected from multiple medical centers and rigorously evaluate its performance on three independent, large-scale test sets. Extensive experiments demonstrate that our method significantly outperforms strong single-task baselines in both accuracy and cross-center robustness, highlighting its superior generalization and clinical applicability.