Using subpicosecond time‐resolved luminescence spectroscopy, we show that the tunneling rate for electrons in an asymmetric double quantum well structure changes dramatically as the energy separation between the two lowest conduction subbands of the coupled well system is tuned through the optical phonon energy. We model these experiments using an ensemble Monte Carlo simulation and obtain a good quantitative agreement between the two. These results demonstrate the importance of phonon‐assisted tunneling processes and raise a number of interesting questions concerning the nature of phonons and carrier‐phonon interactions in these structures.