Abstract: The process of the invention concerns the manufacture of an interposed support of semipermeable microfiltration membranes, the support composed of a permeable mesh and a sealed border of elastomeric material. After deposition of an elastomeric film on a transfer support 2, the assembly which is obtained is cut into one or more elements 3 reconstituting the border; this or these elements 3 are applied on the mesh with their support(s) 2 and the elastomer is turned toward the mesh; then the mesh thus equipped is treated with pressure at a temperature of between 100.degree. and 150.degree. C. to cause the elastomer to penetrate into the mesh and to obtain a smooth border surface on each side of this mesh, allowing for a sealed joint. The product which is obtained is applied to the manufacture of microfiltration units, whether it has to do with ultrafiltration, with gas permeation or with hemodialysis.