Context. During its commissioning phase in 2020, the Spectrometer/Telescope for Imaging X-rays (STIX) on board the Solar Orbiter spacecraft observed 69 microflares. The two most significant events from this set (of GOES class B2 and B6) were observed on-disk from the spacecraft as well as from Earth and analysed in terms of the spatial, temporal, and spectral characteristics. Aims. We complement the observations from the STIX instrument with EUV imagery from SDO/AIA and GOES soft X-ray data by adding imaging and plasma diagnostics over different temperature ranges for a detailed microflare case study that is focussed on energy release and transport. Methods. We used data from the GOES for SXR plasma diagnostics and SDO/AIA for carrying out high-cadence EUV imaging and reconstruction of differential emission measure (DEM) maps of the thermal flare plasma. The reconstructed DEM profiles were used to study the temporal evolution of thermal flare plasma in the kernels and loops independently. We derived the time evolution of the flare plasma parameters (EM, T) and thermal energy from STIX, GOES, and AIA observations. In particular, we studied the STIX spectra to determine the nonthermal emission from accelerated electrons. Results. A spectral fitting of the STIX data shows clear nonthermal emission for both microflares studied here. For both events, the plasma temperature and EM derived from STIX and GOES as well as the reconstructed DEM maps differ in absolute values and timing, with AIA (which is sensitive to lower plasma temperatures) lagging behind. The deduced plasma parameters from either method roughly agree with the values in the literature for microflares as do the nonthermal fit parameters from STIX. This finding is corroborated by the Neupert effect exhibited between the time derivative of the GOES SXR emission and the STIX HXR profiles. For the B6 event, for which such an analysis was possible, the non-thermal energy deduced from STIX roughly coincides with the lower estimates of the thermal energy requirement deduced from the SXR and EUV emissions. Conclusions. The observed Neupert effects and impulsive and gradual phases indicate that both events covered in this study are consistent with the standard chromospheric evaporation flare scenario. For the B6 event on 7 June 2020, this interpretation is further supported by the temporal evolution seen in the DEM profiles of the flare ribbons and loops. For this event, we also find that accelerated electrons can roughly account for the required thermal energy. The 6 June 2020 event demonstrates that STIX can detect nonthermal emission for GOES class B2 events that is nonetheless smaller than the background rate level. We demonstrate for the first time how detailed multi-instrument studies of solar flares can be performed with STIX.