Two spacecraft launched and operated by the European Space Agency are currently performing observations in Mars orbit. For >15 years Mars Express has been conducting global surveys of the surface, the atmosphere and the plasma environment of the Red Planet. The Trace Gas Orbiter, the first element of the ExoMars programme, began its science phase in 2018 focusing on investigations of the atmospheric composition with unprecedented sensitivity as well as surface and subsurface studies. The coordination of observation programmes of both spacecraft aims at cross calibration of the instruments and exploitation of new opportunities provided by the presence of two spacecraft whose science operations are performed by two closely collaborating teams at the European Space Astronomy Centre (ESAC). In this paper we describe the first combined observations executed by the Mars Express and Trace Gas Orbiter missions since the start of the TGO operational phase in April 2018 until June 2019. Also included is the science opportunity analysis that has been performed by the Science Operation Centres and instrument teams to identify the observation opportunities until the end of 2020. These results provide a valuable contribution to the scientific community by enabling collaborations within the instrument teams and enhance the scientific outcome of both missions. This information is also valuable to other Mars missions (MAVEN, Mars Reconnaissance Orbiter, Curiosity, …), which may be interested in observing these locations for wider scientific collaboration. In this work we have analysed the simultaneous and quasi-simultaneous opportunities for cross-calibrations and combined observations by both missions, in particular for the vertical atmospheric profiles with solar occultation and the global atmospheric monitoring with nadir observations. As a result of this work we have identified simultaneous solar occultations that can be combined to compare vertical atmospheric profiles of the same region observed by different instruments within <2 minute difference, and many other quasi-simultaneous occultation observations within 15 minute difference at various latitudes and local times. We have also analysed and identified the simultaneous nadir observations that have been planned regularly at different distances and illumination conditions, and studied the seasonal evolution of the orbital crossing points and the alignment of the ground tracks driven by seasonal orbital variations. Lastly we provide an analysis of future opportunities to improve the global coverage of the atmosphere until the end of 2020. This study includes combined opportunities for nadir, solar occultations and a preliminary study of the coverage for limbs and radio occultations between both spacecraft. The resulting observations strongly increase the robustness of both Mars Express and Trace Gas Orbiter investigations due to cross-calibration of the instruments. They significantly increase spatial and temporal coverage, open new opportunities for scientific collaboration and synergy thus enhancing overall science return of both missions.