Infrared absorption spectroscopy is used to study H-related point defects in H+-implanted Si (Si:H) and Ge (Ge:H). The absorption lines at 743.1, 748.0, 1986.5 and 1989.4 cm-1 in Si:H and at 700.3, 705.5, 1881.8 and 1883.5 cm-1 in Ge:H are shown to originate from the same defect containing two equivalent H atoms. Uniaxial stress experiments show that the defects have monoclinic-II symmetry, and the orientations of the two Si-H or Ge-H bonds are determined. The structure and the local vibrational modes of the self-interstitial binding two H atoms (IH2) are calculated with LDF cluster theory. The symmetry, bond-orientations and isotopic frequency-shifts calculated for IH2 are in excellent agreement with those observed for the 743.1-, 748.0-, 1986.5- and 1989.4-cm-1 modes in Si:H and for the 700.3-, 705.5-, 1881.8- and 1883.5-cm-1 modes in Ge:H.