Transport properties of exchange-biased magnetic tunnel junction structures are reported as a function of tunnel barrier thickness. The temperature dependence of the tunneling conductance and magnetoresistance (MR) is consistent with recent theories relating it to the magnon excitations at the electrode-barrier interface or the temperature-dependent surface magnetization. We have also measured the bias voltage dependence of the MR. For CoFe magnetic electrodes, the reduction in MR is approximately 50% at biases of similar to 250 mV. At low temperatures, we observe a cusp-like dip in the tunneling conductance at zero-bias. The conductance increases as the square-root of the bias voltage, indicating that electron-electron interactions as in disordered media may be important. Coating a magnetic electrode or the oxide barrier with an alternate, thin magnetic layer of higher spin polarization is shown to generally increase the MR by several percent but at the expense of higher 1/f noise.