Local discontinuities may arise in structural concrete due to abrupt changes in the sectional stiffness of connecting elements, construction joints or stress-induced interfaces in both cast-in-place and prefabricated structures. This paper aims at developing a unified path-dependent constitutive model for deformed reinforcing bars crossing such interfaces when subjected to generic three-dimensional displacement paths. The stress transfer mechanism is formulated from a microscopic point of view, and the engineering attention is chiefly directed at coupled cyclic pullout and transverse shear. Systematic verification of the model is carried out by comparing computational predictions with available experimental results.