A drainage-promoting wrap for a building structure includes a weather-resistive membrane having a face with a series of separate, spaced-apart, spacer elements bonded thereto and projecting therefrom to a first predetermined height and an embossed membrane having embossments projecting from a face thereof to a second predetermined height. The weather-resistive membrane and embossed membrane are bonded together to form a double-sided drainage promoting wrap such that the spacer elements project from a first face of the wrap and the embossments project from an opposite face of the wrap. The first predetermined height may be greater than the second predetermined height. Wall and roof assemblies and a method of producing a wrap are also provided.