Quantitative understanding of the sources and sinks of greenhouse gases is essential for predicting greenhouse-gas-climate feedback processes and their impacts on climate variability and change. Australia plays a significant role in driving variability in global carbon cycling, but the budgets of carbon gases in Australia remain highly uncertain. Here, shipborne Fourier transform infrared spectrometer measurements collected around Australia are used together with a global chemical transport model (GEOS-Chem) to analyse the variability of three direct and indirect carbon greenhouse gases: carbon dioxide (CO2), methane (CH4) and carbon monoxide (CO). Using these measurements, we provide an updated distribution of these gases. From the model, we quantify their sources and sinks, and we exploit the benefits of multi-species analysis to explore co-variations to constrain relevant processes. We find that for all three gases, the eastern Australian coast is largely influenced by local anthropogenic sources, while the southern, western and northern coasts are characterised by a mixture of anthropogenic and natural sources. Comparing coincident and co-located enhancements in the three carbon gases highlighted several common sources from the Australian continent. We found evidence for 17 events with similar enhancement patterns indicative of co-emission and calculated enhancement ratios and modelled source contributions for each event. We found that anthropogenic co-enhancement events are common along the eastern coast, while co-enhancement events in the tropics primarily derive from biomass burning sources. While the GEOS-Chem model generally reproduced the timing of co-enhancement events, it was less able to reproduce the magnitude of enhancements. We used these differences to identify underestimated, overestimated and missing processes in the model. We found model overestimates of CH4 from coal burning and underestimates of all three gases from biomass burning. We identified missing sources from fossil fuel, biofuel, oil, gas, coal, livestock, biomass burning and the biosphere in the model, pointing to the need to further develop and evaluate greenhouse-gas emission inventories for the Australian continent.