We present a study of the cosmic infrared background, which is a measure of the dust-obscured activity in all galaxies in the Universe. We venture to isolate the galaxies responsible for the background at 1 mm; with spectroscopic and photometric redshifts we constrain the redshift distribution of these galaxies. We create a deep 1.16 mm map (σ∼ 0.5 mJy) by combining the AzTEC 1.1 mm and MAMBO 1.2 mm data sets in the Great Observatories Origins Deep Survey North (GOODS-N) region. This combined map contains 41 secure detections, 13 of which are new. By averaging the 1.16 mm flux densities of individually undetected galaxies with 24 μm flux densities >25 μJy, we resolve 31-45 per cent of the 1.16 mm background. Repeating our analysis on the SCUBA 850 μm map, we resolve a higher percentage (40-64 per cent) of the 850 μm background. A majority of the background resolved (attributed to individual galaxies) at both wavelengths comes from galaxies at z > 1.3. If the ratio of the resolved submillimetre to millimetre background is applied to a reasonable scenario for the origins of the unresolved submillimetre background, 60-88 per cent of the total 1.16 mm background comes from galaxies at z > 1.3.