The present invention relates to a composite prosthesis for reinforcement of a tissue structure, including a porous textile support which includes an arrangement of threads each composed of at least one filament of nonabsorbable polymer material, said textile support defining a microporous texture including the interstices located between at least two threads at the sites of contact of one thread with at least one other thread, wherein, in at least one protected zone of the textile support, a hydrophilic absorbable material coats the textile support, forming a film enveloping and penetrating into the arrangement of threads, occluding at least the microporous texture, but without forming a plane layer covering at least one face of the textile support.It also relates to a process for preparing such a composite reinforcement prosthesis.