High average-power, nanosecond-duration, laser pulses induce damage on uncoated optics, due in part to an enhanced localized field at the exit surface of the components. Similarly, anti-reflection (AR) thin-film coated optics have similar field enhancement regions, due to multiple boundaries, and experience laser induced damage on both entry and exit interfaces. Sub-wavelength anti-reflection randomly structured surfaces (rARSS) have been shown to have a higher laser-induced damage threshold than traditional AR coatings. Previously published work detailed laser-induced damage on rARSS on a single surface of optical quality, planar, fused silica substrates; optimized for maximum transmission (99.5%) at 1064 nm. The present study explores the introduction of rARSS to both sides of the substrate. Laser-induced damage was systematically created and measured at contiguous locations along the substrate, using 1064 nm wavelength, 6-10 ns duration pulses. Laser output was focused to increase incident irradiance at the initial interface. Incident fluence was directly controlled by Q-switching the laser to create fluence values at, and above, damage thresholds for both entry and exit sides. It was determined that double-sided rARSS substrates have a higher damage threshold than thin-film AR coatings, while they have a lower damage threshold than entrance-only and exit-only sided rARSS (previous study), as well as, lower damage threshold than plain, optical quality, uncoated, fused silica. Damage on the exit-side of the substrate was ballistic in nature, showing surface cracks and outward-oriented debris craters. Contrastingly, damage on the entry-side of the substrate was thermally-induced local-densification of random structures with a latent footprint.