Antibodies safeguard our health through their precise and potent binding to specific antigens, demonstrating promising therapeutic efficacy in the treatment of numerous diseases, including COVID-19. Recent advancements in biomedical language models have shown the great potential to interpret complex biological structures and functions. However, existing antibody specific models have a notable limitation that they lack explicit consideration for antibody structural information, despite the fact that both 1D sequence and 3D structure carry unique and complementary insights into antibody behavior and functionality. This paper proposes Sequence-Structure multi-level pre-trained Antibody Language Model (S$^2$ALM), combining holistic sequential and structural information in one unified, generic antibody foundation model. We construct a hierarchical pre-training paradigm incorporated with two customized multi-level training objectives to facilitate the modeling of comprehensive antibody representations. S$^2$ALM's representation space uncovers inherent functional binding mechanisms, biological evolution properties and structural interaction patterns. Pre-trained over 75 million sequences and 11.7 million structures, S$^2$ALM can be adopted for diverse downstream tasks: accurately predicting antigen-antibody binding affinities, precisely distinguishing B cell maturation stages, identifying antibody crucial binding positions, and specifically designing novel coronavirus-binding antibodies. Remarkably, S$^2$ALM outperforms well-established and renowned baselines and sets new state-of-the-art performance across extensive antibody specific understanding and generation tasks. S$^2$ALM's ability to model comprehensive and generalized representations further positions its potential to advance real-world therapeutic antibody development, potentially addressing unmet academic, industrial, and clinical needs.