The first ground-based experiment to prove the concept of a novel space-based observation technique for microwave and infrared-laser occultation between low-Earth-orbit satellites was performed in the Canary Islands between La Palma and Tenerife. For two nights from 21 to 22 July 2011 the experiment delivered the infrared-laser differential transmission principle for the measurement of greenhouse gases (GHGs) in the free atmosphere. Such global and long-term stable measurements of GHGs, accompanied also by measurements of thermodynamic parameters and line-of-sight wind in a self-calibrating way, have become very important for climate change monitoring. The experiment delivered promising initial data for demonstrating the new observation concept by retrieving volume mixing ratios of GHGs along a ~144 km signal path at altitudes of ~2.4 km. Here, we present a detailed analysis of the measurements, following a recent publication that introduced the experiment's technical setup and first results for an example retrieval of CO₂. We present the observational and validation data sets, the latter simultaneously measured at the transmitter and receiver sites; the measurement data handling; and the differential transmission retrieval procedure. We also determine the individual and combined uncertainties influencing the results and present the retrieval results for ¹²CO₂, ¹³CO₂, C¹⁸OO, H₂O and CH₄. The new method is found to have a reliable basis for monitoring of greenhouse gases such as CO₂, CH₄, and H₂O in the free atmosphere.