A novel thermodynamically consistent cohesive-frictional model for the analysis of interface degradation and failure under either monotonic quasi-static loading or cyclic loading in low-cycle fatigue problems is proposed. Starting from the definition of a suitable Helmholtz energy density function, a phenomenological interface model is developed in the framework of plasticity and damage mechanics. In particular, a coupled plasticitydamage activation function is defined and employed together the consistent evolution rules to capture the evolution of damage and plasticity under the action of the external loads. Due to the specific features of such threshold and flow rules, the initiation and accumulation of damage under monotonic increasing loads is captured and accompanied by negligible plastic evolution, allowing to approximate pure damage-based cohesive laws. On the other hand, coupling associative plasticity and damage evolution allows linking the interface degradation in low-cycle fatigue processes to plastic hysteresis, on the basis of the phenomenological assumption that no infinite plastic flows may happen without microstructural transformation leading to loss of load bearing capability. The model also embodies a smooth transition from an initially cohesive to a residual frictional interface behaviour, governed by a Coulomb frictional activation function. The developed formulation has been implemented and assessed for individual interfaces, highlighting consistent phenomenological behaviour. It has been then applied to the analysis of delamination and de-bonding in composite test cases, showing accuracy against experimental data and confirming its potential.