Cellular porous materials are an attractive choice for lightweight structural design. However, though their open porous architecture is ideally suited for multifunctional applications, their use is typically limited by the pore sizes achievable by traditional as well as advanced fabrication processes. Here, we present an alternative route towards overcoming this pore size limitation by leveraging our recent success in printing fibrous structures. This is achieved by superimposing a fibrous network on a load-bearing, open-celled porous architecture. The multifunctional structure is 3D printed using a novel technique that enables us to simultaneously print a load-bearing scaffold and the necessary fibrous network. The acoustic properties of the printed structures are tested using a normal-incidence impedance tube method. Our results show that such structures can provide very high absorption at low frequencies while retaining the mechanical performance of the underlying architected structure.