The potential-energy surfaces (PESs) and electronic structures of neutral interstitial hydrogen in zinc-blende AlP and SiC are calculated and compared with those previously obtained at the same theoretical level in diamond, Si, and zinc-blende BN and BP. The calculations are done in a variety of clusters at the approximate ab initio Hartree-Fock level with the method of partial retention of diatomic differential overlap. The PES has three minima in each host: near the bond-centered (BC) site, and at the two inequivalent tetrahedral interstitial (T) sites. At the BC site, H0 always forms a stronger bond with the least electronegative atom. The lowest in energy of the two T sites always is the one with the four least electronegative nearest neighbors. In AlP and SiC, the BC site is not the absolute minimum of the PES. Systematic trends in the properties of H0 with the ionic character of the host are apparent. The diffusion characteristics of H in the various hosts are discussed. The equilibrium structures of H0 and H+ are calculated. Our results show that + is (Mu*)+. The various transitions involving + (Mu*'+, Mu'+, or +'Mu) observed in Si, Ge, GaAs, or SiC are consistent with our PESs.