Spin-dependent coherent tunneling has been experimentally observed in high-quality sputtered-deposited ${\text{Co}}_{2}\text{FeAl}/\text{MgO}/\text{CoFe}$ epitaxial magnetic tunneling junctions (MTJs). Consequently, the microfabricated MTJs manifest a very large tunnel magnetoresistance (TMR) at room temperature and an unexpectedly TMR oscillation as a function of MgO barrier thickness. First-principles electronic band calculations confirm the pronounced coherent tunneling effect and are in good agreement with the experimental data. The present work demonstrates the importance of coherent tunneling for large TMR with Heusler alloys