Permeance ratings of a variable perm sheet material, facing, and faced building insulation assembly vary with ambient humidity and/or temperature. In the insulation assembly, a facing is bonded to a major surface of an insulation layer. A central field portion of the facing, as bonded to the insulation layer, has variable water vapor transmission properties that vary from a relatively low permeance when exposed to ambient conditions of low humidity to a relatively high permeance when exposed to ambient conditions of high humidity. Preferably, the facing, as part of an insulation assembly, is fungi growth-resistant and may include a bonding layer, such as a heat activated bonding layer, that bonds the facing to an insulation layer. The sheet material may be embossed to affect its water vapor transmission characteristics.