Systems, methods, and apparatuses for treating a tissue site with reduced pressure are described. The system includes a manifold configured to be placed adjacent the tissue site, and a sealing member configured to be placed over the tissue site and the manifold. The system also includes a reduced-pressure source fluidly coupled to the manifold through the sealing member. The system further includes a pouch having an upstream layer having a first thickness, a downstream layer having a second thickness, and an absorbent member enclosed between the upstream layer and the downstream layer. The second thickness is greater than the first thickness. The upstream layer may have a hydrophilic side adjacent the absorbent member, and the downstream layer may have a hydrophobic side adjacent the absorbent member.