Disclosed is a multilayer film or sheet, which comprises at least one vapor barrier layer and at least one vapor transmission-adjusting layer wherein the vapor transmission-adjusting layer comprises a neutralized acid copolymer or ionomer thereof, an organic acid, and optionally other polymers, having a ratio of wet cup permeance to dry cup permeance greater than 10. The vapor barrier layer comprises ethylene polymer, propylene polymer, polyvinyl alcohol, polyamide, polyester, ethylene vinyl alcohol copolymer, polyvinylidene chloride, PVC, or combinations of two or more thereof. The film is useful as a variable vapor barrier for moisture control of buildings. Also disclosed are articles comprising the multilayer film.