This paper deals with the accurate modelling of unreinforced masonry (URM) behaviour using a 3D mesoscale description consisting of quadratic solid elements for masonry units combined with zero-thickness interface elements, the latter representing in a unified way the mortar and brick–mortar interfaces. A new constitutive model for the unified joint interfaces under cyclic loading is proposed. The model is based upon the combination of plasticity and damage. A multi-surface yield criterion in the stress domain governs the development of permanent plastic strains. Both strength and stiffness degradation are captured through the evolution of an anisotropic damage tensor, which is coupled to the plastic work produced. The restitution of normal stiffness in compression is taken into account by employing two separate damage variables for tension and compression in the normal direction. A simplified plastic yield surface is considered and the coupling of plasticity and damage is implemented in an efficient step by step approach for increased robustness. The computational cost of simulations performed using the mesoscale masonry description is reduced by employing a partitioning framework for parallel computation, which enables the application of the model at structural scale. Numerical results are compared against experimental data on realistic masonry components and structures subjected to monotonic and cyclic loading to show the ability of the proposed strategy to accurately capture the behaviour of URM under different types of loading.