In this paper, we study the size effects on the phonon transmission across material interfaces using the atomistic Green's function method. Layered Si and Ge or Ge-like structures are modeled with a variety of confined sizes in both transverse and longitudinal directions. The dynamical equation of the lattice vibration (phonon waves) is solved using the Green's function method and the phonon transmission is calculated through the obtained Green's function. Phonon transmission across a single interface of semi-infinite Si and Ge materials is studied first for the validation of the methodology. We show that phonon transmission across an interface can be tuned by changing the mass ratio of the two materials. Multi-layered superlattice-like structures with longitudinal size confinement are then studied. Frequency-dependent phonon transmission as a function of both the number of periods and the period thickness is reported. A converged phonon transmission after ten periods is observed due to the formation of phonon minibands. Frequency-dependent phonon transmission with transverse size confinement is also studied for the interface of Si and Ge nanowire-like structures. The phonon confinement induces new dips and peaks of phonon transmission when compared with the results for a bulk interface. With increasing size in the transverse direction, the phonon transmission approaches that of a bulk Si/Ge interface.