Conventional photoacoustic computed tomography (PACT) image reconstruction methods assume that the object and surrounding medium are described by a constant speed-of-sound (SOS) value. In order to accurately recover fine structures, SOS heterogeneities should be quantified and compensated for during PACT reconstruction. To address this problem, several groups have proposed hybrid systems that combine PACT with ultrasound computed tomography (USCT). In such systems, a SOS map is reconstructed first via USCT. Consequently, this SOS map is employed to inform the PACT reconstruction method. Additionally, the SOS map can provide structural information regarding tissue, which is complementary to the functional information from the PACT image. We propose a paradigm shift in the way that images are reconstructed in hybrid PACT-USCT imaging. Inspired by our observation that information about the SOS distribution is encoded in PACT measurements, we propose to jointly reconstruct the absorbed optical energy density and SOS distributions from a combined set of USCT and PACT measurements, thereby reducing the two reconstruction problems into one. This innovative approach has several advantages over conventional approaches in which PACT and USCT images are reconstructed independently: (1) Variations in the SOS will automatically be accounted for, optimizing PACT image quality; (2) The reconstructed PACT and USCT images will possess minimal systematic artifacts because errors in the imaging models will be optimally balanced during the joint reconstruction; (3) Due to the exploitation of information regarding the SOS distribution in the full-view PACT data, our approach will permit high-resolution reconstruction of the SOS distribution from sparse array data.