This paper presents detailed experimental and analytical investigations into the influence of textile-reinforced mortar (TRM) strengthening on the in-plane and out-of-plane response of unreinforced heritage masonry (URM) elements. The URM wall elements consist of hydraulic lime mortar and fired-clay bricks, and the TRM reinforcement employs mortar-embedded layers of alkali age-resistant glass meshes. Apart from the material characterisation tests on mortars, bricks, and TRM coupons, the experimental programme includes axial compression tests on wallettes, diagonal compression tests on square panels, as well as four-point bending tests on rectangular panels. In the latter, the bending loads are applied either parallel or perpendicular to the bed joints in order to assess the joint layout effect on the behaviour. With the aid of digital image correlation, the in-plane and out-of-plane enhancement in stiffness, strength, and ductility of the masonry elements due to the TRM strengthening is quantified, while the TRM influence on the crack patterns and failure modes is also examined. The results show that the number of mesh layers has a significant influence on the behaviour for the out-of-plane bending tests but plays a less pronounced role in the in-plane shear cases. Modified analytical models for the in-plane shear and out-of-plane bending capacities of reinforced masonry elements, of the type examined in this study, are also proposed and assessed alongside existing codified procedures. The application of current code provisions results in overly conservative estimates. In contrast, the proposed analytical approaches for determining the in-plane and out-of-plane strength provide close prediction of the experimental capacities from this study as well as those from a wider collated database of previous tests, and are therefore suitable for implementation in practical assessment and rehabilitation guidelines.