Using an improved nonlocal resonance theory, total cross sections, rovibrational final state distributions and electron spectra for low-energy (< 2 eV) associative detachment (AD) collisions between hydrogen atoms and negative halogen ions X- (X= F, Cl, Br) as well as deuterium atoms and F- ions have been calculated. The model involves realistic long-range interactions for the H + X- systems and takes into account the dependence of the dipole-modified threshold exponent on internuclear distance. Good agreement is found between experimental data for the total AD cross sections and the theoretical results. In the calculated electron energy spectra nonlocal effects are manifest through step structure which is (almost) independent of collision energy; this structure should therefore be observable in experiments with rather modest collision energy resolution. For illustration, electron spectra are presented which correspond to realistic experimental conditions with regard to the energy widths of the electron spectrometer and the collision energy distribution. The rovibrational final state distributions in the formed HX(v,J) molecules are reported for a thermal kinetic energy distribution at T~300 K; for HF, DF, and HCl the rotational-summed vibrational populations P_v are compared with previous theoretical and experimental results.