We present a detailed study of the QSO-galaxy pair SDSS J163956.35+112758.7 (z q = 0.993) and SDSS J163956.38+112802.1 (z g = 0.079) based on observations carried out using the Giant Metrewave Radio Telescope (GMRT), the Very Large Baseline Array (VLBA), the Sloan Digital Sky Survey and the ESO New Technology Telescope. We show that the interstellar medium of the galaxy probed by the QSO line of sight has near-solar metallicity 12+log(O/H) = 8.47 ± 0.25 and dust extinction E(B − V) ∼ 0.83 ± 0.11 typical of what is usually seen in translucent clouds. We report the detection of absorption in the λ6284 diffuse interstellar band (DIB) with a rest equivalent width of 1.45 ± 0.20 Å. Our GMRT spectrum shows a strong 21-cm absorption at the redshift of the galaxy with an integrated optical depth of 15.70 ± 0.13 km s−1. Follow-up VLBA observations show that the background radio source is resolved into three components with a maximum projected separation of 89 pc at the redshift of the galaxy. One of these components is too weak to provide useful 21-cm H i information. The integrated H i optical depth towards the other two components are higher than that measured in our GMRT spectrum and differ by a factor 2. By comparing the GMRT and VLBA spectra we show the presence of structures in the 21-cm optical depth on parsec scales. We discuss the implications of such structures for the spin-temperature measurements in high-z damped Lyman α systems. The analysis presented here suggests that this QSO-galaxy pair is an ideal target for studying the DIBs and molecular species using future observations in optical and radio wavebands.