A process for manufacturing an integrated membrane made of semiconductor material includes the step of forming, in a monolithic body of semiconductor material having a front face, a buried cavity, extending at a distance from the front face and delimiting with the front face a surface region of the monolithic body, the surface region forming a membrane that is suspended above the buried cavity. The process further envisages the step of forming an insulation structure in a surface portion of the monolithic body to electrically insulate the membrane from the monolithic body; and the further and distinct step of setting the insulation structure at a distance from the membrane so that it will be positioned outside the membrane at a non-zero distance of separation.