We studied magnetoresistance (MR) in La2/3Sr1/3MnO3 (LSMO)/organic semiconductor (OSC)/Fe heterojunction devices using rubrene (C42H28) as an organic semiconductor. Efficient spin polarized tunneling using a hybrid barrier (oxide (1.2 nm)/rubrene (5 nm)) was observed. Devices with a thin layer of rubrene as the barrier may have magnetic clusters and/or pinholes in the barrier, which could explain significant variations of MR among devices. As the thickness of the rubrene layer is increased, device current becomes strongly limited by carrier injection resulting in strong temperature and bias dependent device resistance. The carrier injection in these devices can be described with thermionic field emission at the metal/OSC interface and is analyzed with both empirical and theoretical models. The effect of carrier transport through the spacer on the magnetoresistance for organic-based spin valve is discussed. The observed giant magnetoresistance (GMR) in 20 nm rubrene device demonstrates the spin polarized carrier injection and transport through the rubrene OSC layer.