A thermodynamically consistent phase field formulation for modeling the interactions between interfacial damage and bulk brittle fracture is presented. A regularization scheme is considered for both the interface and the crack phase field. A coupled exponential cohesive zone law is adopted to model the interface which has the contributions of both normal and tangential displacement jump components. A novel nonlocal approach is devised to evaluate the smoothened values of jump at the regularized interface using element-specific geometric information. Such a description of the interface allows a more realistic mechanical response of any composite system in terms of accurately representing failure modes such as matrix/bulk cracking, deflection and or branching of crack at interface, through thickness penetration at interface, and delamination. The possibility of these would depend on modulus mismatch, inclination of the interface, length of the interface and relative fracture toughness of the interface to the bulk. Several numerical examples are solved to validate the performance of the proposed model by peel test, crack interaction with an inclined interface, crack at a bimaterial interface, and stiff-soft interface crack interaction. © 2021 Taylor & Francis Group, LLC.