The results of ab initio pseudopotential calculations to study the energetics of hydrogen-double acceptor complexes in crystalline Si and GaAs are presented. Double acceptors considered here are substitutional Be and Ga antisite in Si and GaAs, respectively. For both monatomic- and diatomic-hydrogen-double acceptor complexes, the C site which corresponds to the middle of the rhombus formed by two neighboring double acceptor-host bonds is found to be energetically most favorable for interstitial H atoms as stable position. Furthermore, these double acceptors are completely passivated by two hydrogen atoms in the form of diatomic-H-double acceptor complexes. Microscopic structures of these diatomic-H-double acceptor complexes are that two hydrogen atoms are positioned at two neighboring C sites. Small lattice relaxations are found for both monatomic- and diatomic-H-double acceptor complexes. In a recently proposed [111] substitutional-interstitial Be pair which was shown to be more stable than a single substitutional Be and is electrically inactive, atomic H is also positioned at the C site. A new hydrogen tunneling path going through a M site is proposed with an energy barrier of 0.4 eV.