The availability of in-situ neutral and electron densities along the orbit of the satellite missions GRACE and CHAMP provide a good opportunity to study the ionosphere-thermosphere (IT) system. The aim of this paper is (1) to use these data sets, to study the IT density relation empirically via correlation properties for different conditions depending on solar activity, geomagnetic latitude, and local time and (2) to verify whether these relations are consistent with the output of the TIE-GCM model of the thermosphere and ionosphere. Our results show that the correlations of electron and neutral densities strongly depend on magnetic local time (MLT) with a minimal correlation between 6-9h MLT, e.g., every 131 days for CHAMP around 400km altitude and every 160 days for GRACE around 500km. During low solar activity, the correlation of modeled and measured densities agrees well for both satellites. On the contrary, we note that the correlations between the modeled values are higher, especially during high solar activity, where the difference between correlations of modeled and measured densities is about 0.2. We suggest that the reason for this misalignment might be related to the poor representation of the equatorial density anomaly in the model especially during high solar activity. We believe our results will be useful for studies that aim at assimilating electron densities into a physical model to improve the prediction of neutral densities, since the skill of data assimilation depends to a large extent on the representation of the correlation between both densities.