The invention relates to a hollow membrane (11) comprising two support layers arranged one above the other forming a space between them and a plurality of capillary tubes arranged between the support layers forming capillary channels for the flow of a first fluid, the space between the capillary tubes forming an internal cavity for the circulation of a second fluid around the capillary tubes, and the whole assembly being made of an organic polymer.These membranes (11) can be assembled into modules for the treatment of a fluid with intermediate porous panels (13).