Context. The mass-loss process from evolved stars is a key ingredient for our understanding of many fields of astrophysics, including stellar evolution and the chemical enrichment of the interstellar medium (ISM) via stellar yields. Nevertheless, many questions are still unsolved, one of which is the geometry of the mass-loss process. Aims. Taking advantage of the results from the Herschel Mass loss of Evolved StarS (MESS) programme, we initiated a coordinated effort to characterise the geometry of mass loss from evolved red giants at various spatial scales. Methods. For this purpose we used the MID-infrared interferometric Instrument (MIDI) to resolve the inner envelope of 14 asymptotic giant branch stars (AGBs) in the MESS sample. In this contribution we present an overview of the interferometric data collected within the frame of our Large Programme, and we also add archive data for completeness. We studied the geometry of the inner atmosphere by comparing the observations with predictions from different geometric models. Results. Asymmetries are detected for the following five stars: R Leo, RT Vir, π1Gruis, omi Ori, and R Crt. All the objects are O-rich or S-type, suggesting that asymmetries in the N band are more common among stars with such chemistry. We speculate that this fact is related to the characteristics of the dust grains. Except for one star, no interferometric variability is detected, i.e. the changes in size of the shells of non-mira stars correspond to changes of the visibility of less than 10%. The observed spectral variability confirms previous findings from the literature. The detection of dust in our sample follows the location of the AGBs in the IRAS colour-colour diagram: More dust is detected around oxygen-rich stars in region II and in the carbon stars in region VII. The SiC dust feature does not appear in the visibility spectrum of the U Ant and S Sct, which are two carbon stars with detached shells. This finding has implications for the theory of SiC dust formation.