The selectivity in composite damage sensing using the electrical resistance approach is investigated by deliberately placing multiwall carbon nanotubes dispersed within the matrix or deposited onto the fiber surface. To this aim, unidirectional glass fiber/carbon nanotube/vinyl ester specimens with fibers oriented along (0°) and transverse (90°) to the loading direction are subjected to quasi-static tension up to failure. The electrical resistance changes in the composite are correlated to the mechanical strain and acoustic emission events. Using this approach, it is shown that the electrical signal is able to discern between fiber and matrix (or fiber/matrix interface) damage. The electrical resistance of composites with multiwall carbon nanotubes located within the matrix is capable of tracking matrix-dominated damage but is poorly sensitive to fiber breakage. In contrast, the composites with multiwall carbon nanotube–modified fibers exhibit outstanding sensitivity to fiber- and fiber/matrix interface damage.