Near- and mid-IR absorption spectra of endohedral H2@C60+ have been measured using He-tagging. The samples have been prepared using a "molecular surgery" synthetic approach and were ionized and spectroscopically characterized in the gas phase. In contrast to neutral C60 and H2@C60, the corresponding He-tagged cationic species show distinct spectral differences. Shifts and line splittings in the near- and mid-IR regions indicate the influence of the caged hydrogen molecule on both the electronic ground and excited states. Possible relevance to astronomy is discussed.