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Most standard models for the thermal boundary conductance (TBC) assume isotropic properties and thus are inappropriate for layered and chain-like materials such as graphite, Bi 2 Te 3 , and high density polyethylene (HDPE). To model such anisotropic materials, here a framework is introduced whereby the first Brillouin zone and the iso-energy surfaces of the Debye dispersion relation are both generalized from spherical to ellipsoidal. This model is checked by comparison with the experimental specific heat capacity of graphite and HDPE, as well as the phonon irradiation of graphite calculated from lattice dynamics. The anisotropic TBC model performs at least six times better than the standard isotropic diffuse mismatch model at explaining the measured TBC between graphite and various metals reported by [Schmidt et al., J. Appl. Phys. 107, 104907 (2010).]. The model further reveals an unexpected guideline to engineer the TBC: due to phonon focusing effects, in many cases the TBC across an interface can be increased by reducing a phonon velocity component parallel to the plane of the interface.