The bias voltage and magnetization direction dependent differential conductivity dI∕dV(Vbias) of tunneling junctions with the Heusler compound Co2Cr0.6Fe0.4Al (CCFA) was investigated. The junctions contain AlOx tunneling barriers and Co counter electrodes. A pronounced shoulder in the differential conductivity with parallel electrode magnetization and a sign change of the tunneling magnetoresistance at a bias voltage of ≃±500 mV were the most prominent features observed. The measurements are discussed in the framework of band structure related effects and inelastic excitations. X-ray absorption spectroscopy (XAS-TEY) investigations show that the CCFA/Al interface has an increased Fe content compared to the sputter target composition, presumably due to Fe buffer layer interdiffusion.