This paper presents near-infrared echellette spectra of faint galaxies in the fields around GRB 050820A at redshift z= 2.613 and GRB 060418 at z= 1.490. The spectroscopic data show that both gamma-ray bursts (GRBs) originate in a dynamic environment of interacting galaxies separated by <15 h−1 kpc in projected distance and |Δv| ≲ 60 in line-of-sight velocity. The optical afterglows revealed in early-epoch Hubble Space Telescope images are at least 2.5 h−1 kpc (or 0.4 arcsec) away from the high surface brightness regions of the interacting members, indicating that the GRB events occurred either in the outskirts of a compact star-forming galaxy or in a low surface brightness satellite. Comparisons of the systemic redshifts of the host galaxies and the velocity distribution of absorbing clouds revealed in early-time afterglow spectra further show that the majority of the absorbing clouds are redshifted from these compact star-forming galaxies. These include the gas producing fine-structure absorption lines at physical distances d∼ afew × 100 pc from the GRB afterglow. The lack of blueshifted absorbing clouds and the spatial offset of the GRB event from the star-forming regions make it difficult to attribute the observed large velocity spread (∼200–400 ) of absorbing gas in the GRB host to galactic-scale outflows. We consider a scenario in which the GRB event occurred in a dwarf satellite of the interacting group and interpret the broad absorption signatures in the afterglow spectra as a collective effect of the turbulent halo gas and the host star-forming interstellar medium. We briefly discuss the implications for the absorption properties observed in the afterglow spectra.