In this paper we compare simultaneous extreme ultraviolet (EUV) line intensity and microwave observations of a filament on the disk. The EUV line intensities were observed by the CDS and SUMER instruments on board SOHO and the radio data by the Very Large Array and the Nobeyama radioheliograph. The main results of this study are the following: (1) The Lyman continuum absorption is responsible for the lower intensity observed above the filament in the EUV lines formed in the transition region (TR) at short wavelengths. In the TR lines at long wavelengths the filament is not visible. This indicates that the proper emission of the TR at the filament top is negligible. (2) The lower intensity of coronal lines and at radio wave lengths is due to the lack of coronal emission: the radio data supply the height of the prominence, while EUV coronal lines supply the missing hot matter emission measure (EM). (3) Our observations support a prominence model of cool threads embedded in the hot coronal plasma, with a sheath-like TR around them. From the missing EM we deduce the TR thickness and from the neutral hydrogen column density, derived from the Lyman continuum and Hei absorption, we estimate the hydrogen density in the cool threads.