The recent discovery of high-temperature superconductivity in hydrogen-based compounds under pressure has fueled the hope for the exploration of hydrides with high critical temperatures (${T}_{c}$). In this work, we systematically investigated pressure-stabilized ternary C-Se-H and C-Te-H compounds using the state-of-the-art structure prediction approach in combination with first-principles calculations. As a result, our simulations identified two cubic phases ($\mathrm{CSe}{\mathrm{H}}_{6}$ and ${\mathrm{C}}_{2}\mathrm{Te}{\mathrm{H}}_{8}$) with a metastable stability feature. $Fd\text{\ensuremath{-}}3m$-structured $\mathrm{CSe}{\mathrm{H}}_{6}$ adopted a diamond-type host Se framework with an embedded guest $\mathrm{C}{\mathrm{H}}_{6}$ covalent octahedron, and ${\mathrm{C}}_{2}\mathrm{Te}{\mathrm{H}}_{8}$ with $Fm\text{\ensuremath{-}}3m$ symmetry adopted a face-centered cubic arrangement of ${\mathrm{H}}_{8}$ cubes, which are interlinked by a molecular unit $\mathrm{C}{\mathrm{H}}_{4}$ tetrahedron. Electron-phonon coupling simulations reveal that $\mathrm{CSe}{\mathrm{H}}_{6}$ has high-temperature superconductivity with a ${T}_{c}$ of 80.6 K at 250 GPa. This high superconductivity could be attributed to the fact that the C $2p$, Se $4p$, and H $1s$ electron states near the Fermi energy couple with high-frequency H-associated phonons. Furthermore, ${\mathrm{C}}_{2}\mathrm{Te}{\mathrm{H}}_{8}$ was estimated to have an even higher ${T}_{c}$ of 151.4 K at 300 GPa due to the large average phonon frequency and the strong coupling between C- and H-derived optical phonons and electrons (C $2p$, Te $5p$, and H $1s$) near the Fermi level. The present results shed light on the future exploration of high-temperature superconductivity among multinary hydrides.