Synergistic exploitation of redundant and complementary information from independent observations of the same target remains a major issue in atmospheric remote-sounding and increasing attention is devoted to investigate optimised or innovative methods for the combination of two or more measured data sets. This paper is focusing on the synergy between middle infrared and millimetre-wave limb sounding measurements of atmospheric composition and temperature and reports the results of a study conducted as part of the preparatory activities of the PREMIER (Process Exploration through Measurements of Infrared and millimetre wave Emitted Radiation) mission candidate to the Core Missions of ESA Earth Explorer 7. The activity was based on data acquired by the MIPAS-STR (Michelson Interferometer for Passive Atmospheric Sounding – STRatospheric aircraft) and MARSCHALS (Millimetre-wave Airborne Receivers for Spectroscopic CHaracterisation in Atmospheric Limb Sounding) instruments onboard the high altitude research aircraft M-55 Geophysica during the flight of the PremierEx (PREMIER Experiment) campaign on 10 March 2010 from Kiruna, Sweden for observation of the Arctic upper troposphere and lower stratosphere. The cloud coverage observed along the flight provided representative test cases to evaluate the synergy in three different scenarios: low clouds in the first part, no clouds in the central part and high tropospheric clouds at the end. The calculation of synergistic profiles of four atmospheric targets (i.e., O2, HNO3, H2O and temperature) was performed using a posteriori combination of individual retrieved profiles, i.e., Level 2 (L2) data rather than simultaneous inverse processing of observed radiances, i.e., Level 1 (L1) data. An innovative method of data fusion, based on the Measurement Space Solution (MSS) was applied along with the standard approach of inverse processing of MARSCHALS spectral radiances using MIPAS-STR retrieval products as a priori information (L1 + L2 method). A quantitative estimate and cross-check of the results of MSS and (L1 + L2) data fusion was achieved based on a specific set of quantifiers including the total retrieval error, the number of degrees of freedom, the relative information distribution and the synergy factor.