We design a multispectral transmission waveguide based on phoxonic crystals at midwave infrared (MWIR) frequencies. The phoxonic crystal slot-waveguide architecture is realized using a germanium (Ge)-slot waveguide, surrounded by a supercell array of oxide holes in silicon–germanium (SiGe) membrane tailored photonic and phononic crystal bandgap. The plane wave simulations for both photonic and phononic crystal unit cells were performed to confirm the geometry of the phoxonic supercell. The bandgap analysis shows the capability of the proposed architecture to confine photons of the terahertz frequency range within the slot waveguide by isolating them from the phonons of gigahertz frequency range. The phononic and photonic bandgaps were simultaneously engineered by varying the periodic variation of the density function and dielectric permittivity, respectively. The computational approach shows the suppression in photon-phonon scattering as validated by a uniform transmission of ∼99.8 % over a broad range of 3 to 5 μm wavelengths. The designed phoxonic crystal waveguide can be fabricated with planar processing technology and used in many applications where multispectral control of mid-IR signals is required.