A novel numerical technique for the modelling of interfaces is introduced for the analysis of reinforced brittle materials. The method exploits the partition of unity property of finite element shape functions. By considering finite element shape functions as partitions of unity, extra degrees of freedom are added to the nodes at the interface between the matrix and reinforcement. A gradient-enhanced damage model is used to simulate the continuum response. Numerical results for a three-point bending test and a pull-out test are presented. The numerical procedure proposed here is suitable for a great variety of applications ranging from discrete cracking and steel-concrete interaction in concrete to delamination processes in composite materials.