Abstract: This composite pipe (20) is of the type including an inner tube (2) made of a first thermoplastic material (A), a reinforcement (21) including a metal tape (3) bonded to the inner tube by a first adhesive (61) compatible with the first thermoplastic material, an outer sheath (4) made of a second thermoplastic material (B), bonded to the reinforcement (21) by a second adhesive (62) compatible with the second thermoplastic material. According to the invention the two materials A and B have different chemical natures and, in the connecting region 22 between the strips opposite one another 61a, 62a, respectively, of the first and of the second adhesive, a means of bonding joins these two bands coherently. In an embodiment this means of bonding consists of adhesives which are different but compatible and co-crosslinked with each other.