Biological composite materials are known to be tough, stiff, stable, viscoelastic bodies, that can creep, recover, absorb energy, and filter vibrations. Their multifunctionality is associated with their architectures, which often consist of mineral units surrounded by organic interfaces that play a key role in the performance of the entire composite. However, the confinement and small dimensions of these organic interfaces pose a challenge in measuring their physical properties by direct methods. We propose an indirect, experimental-analytical framework by which to probe the elastic and viscoelastic behavior of an individual interface. We demonstrate this framework on thin organic interfaces in the shell Pinna nobilis, and discuss its possible uses in various other micro- and nanoscale composite systems.