Midinfrared spectra of the Br-81(-)-H-2 and I--H-2 anion complexes are measured in the H-H stretch region by monitoring the production of halide anion photofragments. The spectra, which are assigned to complexes containing ortho H-2, exhibit rotationally resolved Sigma-Sigma bands whose origins are redshifted from the molecular hydrogen Q(1)(1) transition by 110.8 cm-1 (Br--H-2) and 74.1 cm-1 (I--H-2). The complexes are deduced to possess linear equilibrium structures, with vibrationally averaged intermolecular separations between the halide anion and H-2 center of mass of 3.461 A (Br--H-2) and 3.851 A (I--H-2). Vibrational excitation of the H-2 subunit causes the intermolecular bond to stiffen and contract by 0.115 A (Br--H-2) and 0.112 A (I--H-2). Rydberg-Klein-Rees inversion of the spectroscopic data is used to generate effective radial potential energy curves near the potential minimum that are joined to long-range potential energy curves describing the interaction between an H-2 molecule and a point negative charge. From these curves the dissociation energies of Br--H-2 and I--H-2 with respect to isolated H-2 (j=1) and halide fragments are estimated as 365 and 253 cm-1, respectively.