With the Hubble Space Telescope (HST) and the Goddard High Resolution Spectrograph we have observed four barium and three weak barium stars in the ultraviolet spectral region, together with two nonpeculiar giant standard stars. An additional suspected Ba star was observed with HST and the Space Telescope Imaging Spectrograph. In the H-R diagram, three of the observed Ba stars lie on the same evolutionary tracks as the Hyades giants. Using International Ultraviolet Explorer (IUE) spectra of previously studied giants together with our HST spectra, we investigate whether the chromospheric and transition layer emission-line spectra of the Ba stars are different from those of nonpeculiar giants and from those of giants with peculiar carbon and/or nitrogen abundances. Except for the Ba star HD 46407 and the suspected Ba star HD 65699, the Ba star and mild Ba star emission-line fluxes are, for a given effective temperature and for a given luminosity, lower than those for the nonpeculiar giants observed with IUE. In comparison with the HST-observed standard stars, the C IV λ1550-to-C II λ1335 line flux ratios are smaller, but not necessarily so in comparison with all IUE-observed nonpeculiar giants. However, the C IV-to-C II line flux ratios for the Ba stars decrease with increasing carbon abundances. This shows that the energy balance in the lower transition layer is influenced by the carbon abundance. The temperature gradient appears to be smaller in the C II line-emitting region. There does not seem to be a difference in chromospheric electron densities for the Ba and non-Ba stars, though this result is rather uncertain. Based on observations with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.