We present a comprehensive set of spectral data from two quiescent solar prominences observed in parallel from space and ground: with the VTT, simultaneous two-dimensional imaging of Hβ 4862Å and Ca ii 8542Å yields a constant ratio, indicating small spatial pressure variations over the prominence. With the Gregory, simultaneous spectra of Ca ii 8542Å and He i 10830Å were taken, their widths yielding 8000 < T kin < 9000 K and v nth < 8km/s. The intensity ratio of the helium triplet components gives an optical thickness of τ < 1.0 for the fainter and τ ≤ 2.0 for the brighter prominence. The τ 0 values allow to deduce the source function for the central line intensities and thus the relative population of the helium 3 S and 3 P levels with a mean excitation temperature T mean ex = 3750 K. With SUMER, we sequentially observed 6 spectral windows containing higher Lyman lines, 'cool' emission lines from neutrals and singly charged atoms, as well as 'hot' emission lines from ions like O iv, O v, N v, S v and S vi. The EUV lines show pronounced maxima in the main prominence body as well as 'sidelocations' where the 'hot' lines are enhanced with respect to the 'cool' lines. The line radiance of 'hot' lines blue-wards of the Lyman series limit (λ < 912Å) appear reduced in the main prominence body.This absorption is also visible in TRACE images of Fe ix/x 171Å as fine dark structure which covers only parts of the main ('cool') prominence body.The Lyman lines show a smooth decrease of line widths and radiance with increasing upper level k = 5 through 19. For 5 ≤ k ≤ 8 the level population follows a Boltzmann distribution with T ex > 6 · 10 4 K; higher levels k> 8 appear more and more overpopulated. The larger widths of the Lyman lines require high non-thermal broadening close to that of 'hot' EUV lines. In contrast, the He ii emission is more related to the 'cool' lines.