Current‐voltage behavior is studied experimentally in a Hg0.78Cd0.22Te‐CdTe‐Hg0.78Cd0.22Te heterostructure grown by molecular beam epitaxy. At temperatures above 160 K, energy‐band diagrams suggest that the dominant low‐bias current is thermionic hole emission across the CdTe barrier layer. This interpretation yields a direct determination of 390±75 meV for the HgTe‐CdTe valence‐band discontinuity at 300 K. Similar analyses of current‐voltage data taken at 190–300 K suggest that the valence‐band offset decreases at low temperatures in this heterojunction.