This work focuses on XFEM modeling of elastodamaging interfaces characterized by regularized kinematics. After regularization of the displacement discontinuity, a process zone of finite width with continuous strain fields emerges. The stress fields are independently energy-deduced, modeled via specific constitutive laws, and subsequently introduced within the virtual work principle. The methodology can address cohesive interfaces with vanishing and finite thickness in a unified way. Two-dimensional results for a strain localization problem and several delamination tests are discussed in detail and compared with previous numerical/experimental results.