This work presents a multiscale, thermodynamically consistent framework for modeling damage in bonded structures with strong tension–compression asymmetry. Starting from a thin damaging interphase, two new cohesive-type interface models (F1d and F2d) are derived by asymptotic analysis. The F1d model employs a single damage variable with an asymmetric evolution law, while the F2d model introduces separate tensile and compressive damage variables, allowing independent degradation mechanisms. To establish a physical link between macroscopic interface damage and micro-defect evolution within the adhesive layer, both models are coupled with micromechanical homogenization schemes, namely the Kachanov–Sevostianov non-interacting model and the Mori–Tanaka–Benveniste model, which incorporates defect interactions. The theoretical formulations are validated through numerical simulations of an adhesively bonded joint under axial loading, demonstrating the ability of the proposed approach to capture asymmetric damage behavior and scale-bridging effects in quasi-brittle interfaces.