An experimental campaign on six FRCM systems coupling dry or coated AR glass fiber textile with cement, lime, and gypsum matrices was carried out through characterization tests on constituents and bond tests on composite joints adhered to brick. The analytical model employed to interpret test results includes, differently from the available ones, mortar deformability assuming a trilinear cohesive material law (CML) which governs the matrix-fiber pure mode II interface. Results of single shear test (SST) show that part of the dry textile yarns break and that coating provides marked brittleness and improved capacity to the interface. The interfaces’ unevenness is tackled consistently with the SST setup through the deformable-mortar model. The internal matrix-textile interface activates earlier compared to the external, and the portion of the joint showing a debonded interface at peak load is longer compared to that predicted by the rigid model.