Adhesives are extensively used in industry and construction, with formaldehyde-free options gaining popularity due to their enhanced safety and chemical stability. However, their water resistance remains a significant limitation. In this study, a simple and efficient strategy based on a physicochemical dual cross-linking synergistic network was proposed to develop a new formaldehyde-free adhesive (IBMP-BT). The unique structure, featuring stable chemical cross-linking formed by amidation and a network of multiple hydrogen bonds, enables enhanced water resistance, strength, and toughness of the adhesive. The dry shear strength and toughness of the IBMP-BT adhesive reached 2.03 MPa and 0.600 J, respectively, representing improvements of 89.7% and 255.03% compared to those of the unmodified adhesive. The wet bonding strength of the IBMP-BT adhesive was 1.16 MPa, significantly exceeding the requirements of China's national standards. This innovative network design allows olefin copolymers to replace traditional formaldehyde-based products, leading to the creation of high-performance adhesives.