Context. Studying the coma environment of comet 67P/Churyumov-Gerasimenko (67P) is one of the primary scientific goals of the VIRTIS experiment on the ESA Rosetta mission. Aims. The distribution and variability of water vapour and carbon dioxide in the comet's coma are needed to estimate their production rate, abundances in the nucleus, and the spatial distribution of the active regions. Methods. Infrared emission lines from vibrational bands of water and carbon dioxide at 2.67 and 4.27 mu m, respectively, were observed by the VIRTIS-M imaging channel and mapped from close to the nucleus up to similar to 10 km altitude with a resolution of similar to 40 m/px. A dataset consisting of 74 observations in the 1 5 mu m spectral range acquired from 8 to 14 April 2015 when 67P was at a heliocentric distance of 1.9 AU is analysed in this work. A statistical correlation between the gas distribution and the surface's active regions was performed. Results. The maximum H2O emission is observed within 3 km from the nucleus and is mainly concentrated above two active regions, Aten-Babi and Seth-Hapi, while the CO2 distribution appears more uniform with significant emissions coming from both the "head" and southern latitude regions. In the equatorial region, the column densities of both species decrease with altitude, although CO2 decreases more rapidly than H2O. The calculated CO2/H2O column density ratios above Aten-Babi and Seth-Hapi are 2.4 +/- 0.6% and 3.0 +/- 0.7%, respectively. A value equal to 3.9 +/- 1.0% is observed at equatorial latitudes in the region encompassing Imothep. Conclusions. VIRTIS-M has mapped the distribution of water vapour and carbon dioxide around the nucleus of 67P with unprecedented spatial resolution. The different water and carbon dioxide outgassing above the surface, seen in the VIRTIS-M data, might be indicative of a different thermal history of the northern and southern hemispheres of 67P.