We analyse the near-infrared interline sky background, OH and O2 emission in 19 h of H-band observations with the GNOSIS OH-suppression unit and the IRIS2 spectrograph at the 3.9-m Anglo-Australian Telescope. We find that the long-term behaviour of OH emission is best described by a gradual decrease during the first half of the night followed by a gradual increase during the second half of the night following the behaviour of the solar elevation angle. We measure the interline background at 1.520 μm where the instrumental thermal background is very low and study its variation with zenith distance, time after sunset, ecliptic latitude, lunar zenith distance and lunar distance to determine the presence of non-thermal atmospheric emission, zodiacal scattered light and scattered moonlight. Zodiacal scattered light is too faint to be detected in the summed observations. Scattered moonlight due to Mie scattering by atmospheric aerosols is seen at small lunar distances (ρ ≲ 11°), but is otherwise too faint to detect. Except at very small lunar distances the interline background at a resolving power of R ≈ 2400 when using OH-suppression fibres is dominated by a non-thermal atmospheric source with a temporal behaviour that resembles atmospheric OH emission, suggesting that the interline background contains instrumentally scattered OH. However, the interline background dims more rapidly than OH early in the night, suggesting contributions from rapid dimming molecules. The absolute interline background is 560 ± 120 photons s-1 m-2 μm-1 arcsec-2 under dark conditions. This value is similar to previous measurements without OH suppression, suggesting that non-suppressed atmospheric emission is responsible for the interline background level. Future OH-suppression fibre designs may address this by the suppression of more sky lines usingmore accurate sky-linemeasurements taken from high-resolution spectra.