In this paper, the standardized characterization of nanofibrous membranes used to coat three porous bulk acoustical materials (melamine foam, a polyester textile, and an MDF perforated panel) is presented. The membranes were manufactured from recyclable Polyamide 6 (PA6) and water-soluble polyvinyl alcohol (PVA) using the needleless electrospinning technique. This resulted in very thin membranes that had high porosity and very high airflow resistivity. The membranes were collected in a high-permeability nonwoven substrate. Measured results in both an impedance tube and a reverberation room showed significant improvements in the sound absorption performance of the bulk materials after incorporating the nanofibrous layer. The application of the membranes on the surface of a traditional air-backed perforated panel also improved the sound absorption, exhibiting a broad peak of sound absorption in the low-frequency range. This was particularly true when the membrane area weight was increased. It is concluded that these materials, manufactured as described in this paper, can be alternatives to glass, mineral, and ceramic fibrous materials, which have high carbon footprints.