Despite recent advances in bone adhesives applied for full median sternotomy, the regeneration of bone defects has remained challenging since the healing process is hampered by poor adhesiveness, limited bioactivity, and lack of antibacterial functions. Bioinspired adhesives by marine organisms provide a novel concept to circumvent these problems. Herein, a dual cross-link strategy is employed in designing a multifaceted bioinspired adhesive consisting of a catechol amine-functionalized hyperbranched polymer (polydopamine-co-acrylate, PDA), bredigite (BR) nanoparticles, and Fe3+ ions. The hybrid adhesives exhibit strong adhesion to various substrates such as poly(methyl methacrylate), glass, bone, and skin tissues through synergy between irreversible covalent and reversible noncovalent cross-linking, depending on the BR content. Noticeably, the adhesion strength of hybrid adhesives containing 2 wt % BR nanoparticles to bone tissues is 2.3 ± 0.8 MPa, which is about 3 times higher than that of pure PDA adhesives. We also demonstrate that these hybrid adhesives not only are bioactive and accelerate in vitro bone-like apatite formation but also exhibit antibacterial properties against Staphylococcus aureus, depending on the BR concentration. Furthermore, the superior cellular responses in contact with hybrid adhesives, including improved human osteosarcoma MG63 cell spreading and osteogenic differentiation, are achieved owing to the appropriate ion release and flexibility of the cross-linked double-network adhesive. In summary, multifunctional hybrid PDA/BR adhesives with appreciable osteoconductive, mechanical, and antibacterial properties represent the potential applications for median sternotomy surgery as a bone tissue adhesive.