Fabricating a composite material part comprises the steps of making a consolidated fiber preform, the fibers of the preform being carbon or ceramic fibers that are coated in an interphase formed by at least one layer of pyrolytic carbon (PyC) or of boron-doped carbon (BC). Obtaining a partially densified consolidated fiber preform, where partial densification comprises forming a first matrix phase on the interphase, the first matrix phase comprising a plurality of layers of self-healing material alternating with one or more layers of PyC or of BC. Continuing densification by dispersing carbon and/or ceramic powder within the partially densified consolidated preform and by infiltrating molten silicon or a liquid composition formed for the most part of silicon.