An underlayment membrane between a base surface and an outer coating of a building surface includes a base layer and multiple protrusions extending from the base layer to retain conditioning elements. The protrusions define a plurality of paths, between their side walls for the conditioning elements, which include: first straight portions defined by pairs of protrusions positioned side by side and spaced apart by a distance at most equal to the thickness of the conditioning elements, to hold them by friction; one or more second corrugated portions defined by two or more protrusions spaced apart by a predefined distance greater than the thickness of the conditioning elements and arranged in pairs aligned along lines, which obliquely intersect the path so that a conditioning element is retained by elastic-mechanical contrast with the side walls of the protrusions, the first and second portions of the paths being aligned with each other.