We present experimental measurements of photodesorption from ices of astrophysical relevance. Layers of benzene and water ice were irradiated with a laser tuned to an electronic transition in the benzene molecule. The translational energy of desorbed molecules was measured by time-of-flight (ToF) mass spectrometry. Three distinct photodesorption processes were identified: a direct adsorbate-mediated desorption producing benzene molecules with a translational temperature of around 1200 K, an indirect adsorbate-mediated desorption resulting in water molecules with a translational temperature of around 450 K, and a substrate-mediated desorption of both benzene and water producing molecules with translational temperatures of around 530 and 450 ...