Under the Paris Agreement, countries report their anthropogenic greenhouse gas emissions in national inventories, which are used to track progress towards mitigation goals, but they must be independently verified. Atmospheric observations of CO2, interpreted using inverse methods, can potentially provide that verification. Conventional CO2 inverse methods infer natural CO2 fluxes by subtracting a priori estimates of fuel combustion from the a posteriori net CO2 fluxes, assuming that a priori knowledge for combustion emissions is better than for natural fluxes. We describe an inverse method that uses measurements of CO2 and carbon monoxide (CO), a trace gas that is co-emitted with CO2 during combustion, to report self-consistent combustion emissions and natural fluxes of CO2. We use an ensemble Kalman filter and the GEOS-Chem atmospheric transport model to explore how satellite observations of CO and CO2 collected by the TROPOspheric Monitoring Instrument (TROPOMI) and Orbiting Carbon Observatory-2 (OCO-2), respectively, can improve understanding of combustion emissions and natural CO2 fluxes across the UK and mainland Europe in 2018–2021. We assess the value of using satellite observations of CO2, with and without CO, above what is already available from the in situ network. Using CO2 satellite observations leads to small corrections to a priori emissions that are inconsistent with in situ observations, due partly to the insensitivity of the atmospheric CO2 column to CO2 emission changes. When we introduce satellite CO observations, we find better agreement with our in situ inversion and a better model fit to atmospheric CO2 observations. Our regional mean a posteriori combustion CO2 emission ranges from 4.6–5.0 Gt a−1 (1.5 %–2.4 % relative standard deviation), with all inversions reporting an overestimate for Germany's wintertime emissions. Our national a posteriori CO2 combustion emissions are highly dependent on the assumed relationship between CO2 and CO uncertainties, as expected. Generally, we find better results when we use grid-scale-based a priori CO2:CO uncertainty estimates rather than a fixed relationship between the two species.