Cohesive interfaces appear in many materials or structures, e.g. composites or adhesive bonds. Originally introduced to model crack tips in fracture mechanics, cohesive zone models are used to describe the constitutive behavior of cohesive interfaces since the early 1990s. In the present contribution, the concept of generalized standard materials (GSM) is transferred from the modeling of bulk behavior to cohesive zones. The potential-based framework obtained hereby is referred to as standard dissipative cohesive zones (SD-CZ). Within this framework, an irreversible interface model is developed for the one-dimensional case and subsequently extended to three-dimensional transverse isotropy. While the potential structure of the constitutive law may be required for certain applications, it also brings benefits with regard to the numerical implementation. To the best knowledge of the authors, this is the first approach to interface modeling in a GSM-like framework, where dissipative effects like damage and softening are considered as well as normal-tangential coupling for mixed-mode decohesion. Comparisons to experimental data and existing cohesive zone models outline the capabilities of the approach.