In this paper we study the extended atmosphere of the late-type supergiant alpha Orionis. Infrared spectroscopy of red supergiants reveals strong molecular bands, some of which do not originate in the photosphere but in a cooler layer of molecular material above it. Lately, these layers have been spatially resolved by near and mid-IR interferometry. In this paper, we try to reconcile the IR interferometric and ISO-SWS spectroscopic results on a Orionis with a thorough modelling of the photosphere, molecular layer(s) and dust shell. From the ISO and near-IR interferometric observations, we find that a Orionis has only a very low density water layer close above the photosphere. However, mid-IR interferometric observations and a narrow-slit N-band spectrum suggest much larger extra-photospheric opacity close to the photosphere at those wavelengths, even when taking into account the detached dust shell. We argue that this cannot be due to the water layer, and that another source of mid-IR opacity must be present. We show that this opacity source is probably neither molecular nor chromospheric. Rather, we present amorphous alumina (Al2O3) as the best candidate and discuss this hypothesis in the framework of dust-condensation scenarios.