Antigen-antibody binding is a critical process in the immune response. Although recent progress has advanced antibody design, current methods lack a generative framework for end-to-end modeling of full-atom antibody structures and struggle to fully exploit antigen-specific geometric information for optimizing local binding interfaces and global structures. To overcome these limitations, we introduce AbFlow, a flow-matching framework that leverages optimal transport to design full-atom antibodies end-to-end. AbFlow incorporates an extended velocity field network featuring an equivariant Surface Multi-channel Encoder, which uses surface-level antigen interaction data to refine the antibody structure, particularly the CDR-H3 region. Extensive experiments in paratoep-centric antibody design, multi-CDRs and full-atom antibody design, binding affinity optimization, and complex structure prediction show that AbFlow produces superior antigen-antibody complexes, especially at the contact interface, and markedly improves the binding affinity of generated antibodies.