The morphology of the migrating terdiurnal tide with zonal wavenumber 3 (TW3) in the mesosphere and lower thermosphere (MLT) is revealed using the TIMED satellite datasets from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) and the TIMED Doppler Interferometer (TIDI) instruments from 2002 to 2009, as well as the Thermosphere Ionosphere Mesosphere Electrodynamics General Circulation Model (TIME-GCM). The annual mean structures of the TW3 from the TIME-GCM clearly resemble the first real symmetric (3,3) Hough mode. The TW3 temperature and zonal wind components have three peaks at midlatitudes and near the equator, while the TW3 meridional wind components show four peaks at mid and low latitudes. These features are consistent with those resolved in SABER temperature and TIDI zonal wind above ~95 km. TW3 components in the TIME-GCM are stronger during winter and spring months at midlatitudes, which is in agreement with previous ground-based radar measurements. On the other hand, TW3 components of temperature, zonal and meridional winds from SABER and TIDI display different seasonal variations at different altitudes and latitudes. The results presented in this paper will provide an observational basis for further modeling study of terdiurnal tide impacts on the thermosphere and ionosphere.