We analyzed the 2.6 mm CO and 21 cm H i lines toward the Magellanic superbubble 30 Doradus C, in order to reveal the associated molecular and atomic gas. We uncovered five molecular clouds in a velocity range from 251 to 276 km s−1 toward the western shell. The non-thermal X-rays are clearly enhanced around the molecular clouds on a parsec scale, suggesting possible evidence for magnetic field amplification via shock-cloud interaction. The thermal X-rays are brighter in the eastern shell, where there are no dense molecular or atomic clouds, opposite to the western shell. The TeV γ-ray distribution may spatially match the total interstellar proton column density as well as the non-thermal X-rays. If the hadronic γ-ray is dominant, the total energy of the cosmic-ray protons is at least erg with the estimated mean interstellar proton density ∼60 cm−3. In addition, the γ-ray flux associated with the molecular cloud (e.g., MC3) could be detected and resolved by the Cherenkov Telescope Array (CTA). This should permit CTA to probe the diffusion of cosmic-rays into the associated dense ISM.