We report on the propagation of coherent acoustic wave packets in (001) surface oriented Al0.3Ga0.7As/GaAs heterostructure, generated through localized femtosecond photoexcitation of the GaAs. Transient structural changes in both the substrate and film are measured with picosecond time-resolved x-ray diffraction. The data indicate an elastic response consisting of unipolar compression pulses of a few hundred picosecond duration traveling along [001] and [001] directions that are produced by predominately impulsive stress. The transmission and reflection of the strain pulses are in agreement with an acoustic mismatch model of the heterostructure and free-space interfaces.