A fabric sleeve for protecting elongate members against at least one of EMI, RFI or ESD and method of construction thereof is provided. The sleeve includes a wall extending along a longitudinal axis between opposite ends. The wall is formed from a plurality of filaments interlaced with one another, with at least one of the filaments being provided as a continuous strand of conductive wire and at least some of the filaments being provided as heat-fusible nonconductive filaments. The heat-fusible nonconductive filaments abut the continuous strand of conductive wire at a plurality of bond joints. The continuous strand of conductive wire is at least partially embedded in bonded, fixed attachment with the heat-fusible nonconductive filaments at the bond joints.