Abstract: Carbon-based molecular semiconductors are explored for application in spintronics because their small spinorbit coupling promises long spin lifetimes. We calculate the electronic transport from first principles through spin valves comprising bi-and tri-layers of the fullerene molecules C-60 and C-70, sandwiched between two Fe electrodes. The spin polarization of the current, and the magnetoresistance depend sensitively on the interactions at the interfaces between the molecules and the metal surfaces. They are much less affected by the thickness of the molecular layers. A high current polarization (CP > 90%) and magnetoresistance (MR > 100%) at small bias can be attained using C-70 layers. In contrast, the current polarization and the magnetoresistance at small bias are vanishingly small for C-60 layers. Exploiting a generalized Julliere model we can trace the differences in spin-dependent transport between C-60 and C-70 layers to differences between the molecule-metal interface states. These states also allow one to interpret the current polarization and the magnetoresistance as a function of the applied bias voltage.