The present invention provides an intermediate material composed of an assembly of overlapping and interlaced tapes, characterized in that at least some of the tapes, preferably all of the tapes, known as veiled tapes, are composed of a series of reinforcing yarns or filaments that extend in a direction parallel to the length of the tape to form a unidirectional sheet that is associated on each of its faces with a nonwoven formed from thermoplastic fibers, said two nonwovens providing said veiled tape with cohesiveness because of their thermoplastic nature, to a production method using said material for producing composite parts, and to the composite parts obtained.