The strengthening intervention strategies that exist for masonry buildings are based on the use of thin composites and are a recent activity used in structural engineering. Nowadays, mortar matrices are frequently found instead of epoxy resins, since the fiber reinforced cementitious matrix (FRCM) composites are more compatible with masonry than fiber reinforced plastic (FRP) ones. The mortar matrix in FRCM composites is not comparable to the epoxy resin, and therefore its contribution is different not only in traction but above all on the compression side. Due to its larger thickness, if compared to the epoxy resin, the impact of the mortar matrix on the flexural response of strengthened cross sections is not negligible. This paper aimed to investigate the influence of the contribution of the mortar matrix on the compression side on the flexural capacity of strengthened cross section. As such, p–m interaction domains and bending moment–curvature diagrams were evaluated to understand the influence of several mechanical properties of fiber and mortar matrices on FRCM efficiency, typical of real applications. Hence, the impact of several constitutive relationships of composites (linear and bilinear behavior) was considered for the structural analysis of the strengthened cross section. The presented results are all completely in a dimensionless form; therefore, independent of geometry and mechanical parameters can be the basis for developing standardized design and/or verification methodologies useful for the strengthening systems for masonry elements.