For unreinforced concrete structures utilizing H-shaped steel as a skeletal framework, concrete specimens integrated with H-shaped steel were prepared to represent varying degrees of corrosion, specifically rates of 0%, 5%, 10%, 15%, and 20%. Push-out tests were conducted to analyze the bond stress-slip relationship between H-shaped steel and concrete under different corrosion levels at the interface. An experimental method is proposed to derive the distribution of bond stress across the steel-concrete interface by measuring the compressive displacement on the surface of the concrete. Based on the observations from the tests, four microscopic mechanisms were proposed: chemical bonding, microscopic mechanical bonding, macroscopic mechanical bonding, and rust interface bonding, to explain the impact of corrosion on the bond performance of H-shaped steel in concrete. A constitutive relationship was constructed, incorporating the effect of the corrosion rate on bond stress slip, and an interface damage parameter was introduced to analyze the evolution of interface damage under varying corrosion rates. The research results indicated that the initial bond stiffness at the H-shaped steel-concrete interface increases with the corrosion rate. However, after reaching peak stress, the rate of decline in interface stiffness accelerates with increased corrosion. Notably, at higher corrosion rates (≥15%), the bond-slip curve displays a dual-peak feature, first ascending, then descending, followed by another rise, and ultimately declining. As the corrosion rate increases, the roles of chemical bonding and microscopic mechanical bonding become more dominant, while the contributions of macroscopic mechanical bonding and rust interface bonding diminish. The developed constitutive relationship, validated through comparative analysis with existing models, accurately describes the bond characteristics at the corroded H-shaped steel-concrete interface. Although an increase in corrosion rate hastens the reduction of interface stiffness, its influence on the extent of damage observed upon specimen failure is relatively limited.