Molecular heterojunctions, such as the one based on copper phthalocyanine (CuPc) and carbon fullerene (C-60) molecules, are commonly employed in organic photovoltaic cells as electron donor-acceptor pairs. We have investigated the different atomic structures and electronic and optical properties of the C-60/CuPc heterojunction through first-principles calculations based on density functional theory (DFT) and time-dependent DFT. In general, configurations with the CuPc molecule "lying down" on C-60 are energetically more favorable than configurations with the CuPc molecule "standing up". The lying-down configurations also facilitate charge transfer between the two molecules, due to the stronger interaction and the larger overlap between electronic wavefunctions at the interface. The energetically preferred structure consists of CuPc placed so that the Cu atom is above a bridge site of C-60, with one N-Cu-N bond of CuPc being parallel to a C-C bond of C-60. We also considered the structure of a periodic CuPc monolayer deposited on the (001) surface of a face-centered cubic (fcc) crystal of C-60 molecules with the lying-down orientation and on the (111) surface with the standing-up configuration. We find that the first arrangement can lead to larger open circuit voltage due to an enhanced electronic interaction between CuPc and C-60 molecules.