We present the first calculations of the equilibrium configurations, potential-energy surfaces (PES), and electronic structures of an impurity (neutral interstitial hydrogen) in zinc-blende BN and BP. The host crystals are described by clusters and the calculations are done at an approximate ab initio Hartree-Fock level with the method of partial retention of diatomic differential overlap. The PES for H0 has three minima in each host: near the center of a covalent bond (with H primarily bound to the group-III atom) and at the two tetrahedral interstitial sites. The three sites are energetically comparable in BP but quite different in BN. The chemical structure of bond-centered H0 in III-V compounds is quite different from that in group-IV hosts. The properties of H0 in BN and BP are discussed in terms of the difference of ionicity between the two hosts. The characteristics of muon-spin relaxation (SR) spectra are predicted and qualitatively compared to the experimental data in GaP and GaAs.