Aims. The aim of this work is to analyse the multi-instrument observations of the June 22, 2010 prominence to study its structure in detail, including the prominence-corona transition region and the dark bubble located below the prominence body. Methods. We combined results of the 3D magnetic field modelling with 2D prominence fine structure radiative transfer models to fully exploit the available observations. Results. The 3D linear force-free field model with the unsheared bipole reproduces the morphology of the analysed prominence reasonably well, thus providing useful information about its magnetic field configuration and the location of the magnetic dips. The 2D models of the prominence fine structures provide a good representation of the local plasma configuration in the region dominated by the quasi-vertical threads. However, the low observed Lyman-α central intensities and the morphology of the analysed prominence suggest that its upper central part is not directly illuminated from the solar surface. Conclusions. This multi-disciplinary prominence study allows us to argue that a large part of the prominence-corona transition region plasma can be located inside the magnetic dips in small-scale features that surround the cool prominence material located in the dip centre. We also argue that the dark prominence bubbles can be formed because of perturbations of the prominence magnetic field by parasitic bipoles, causing them to be devoid of the magnetic dips. Magnetic dips, however, form thin layers that surround these bubbles, which might explain the occurrence of the cool prominence material in the lines of sight intersecting the prominence bubbles.