We report extensive VLA and ATCA observations of the two diffuse radio sources in the cluster of galaxies Abell 548b, which confirm their classification as relics. The two relics (named A and B) show similar flux density, extent, shape, polarization and spectral index and are located at projected distances of about 430 and 500 kpc from the cluster center, on the same side of the cluster's X-ray peak. On the basis of spectral indices of discrete radio sources embedded within the diffuse features, we have attempted to distinguish emission peaks of the diffuse sources from unrelated sources. We have found that both relics, in particular the B-relic, show possible fine structure, when observed at high resolution. Another diffuse source (named C) is detected close in projection to the cluster center. High-resolution images show that it contains two discrete radio sources and a diffuse component, which might be a candidate for a small relic source. The nature and properties of the diffuse radio sources are discussed. We conclude that they are likely related to the merger activity in the cluster. Comment: Accepted for publication in MNRAS. 11 pages, 7 figures. Some figures are degraded to reduce their size. A version with high resolution images is available at http://www.ira.inaf.it/~lferetti/OUTGOING/papA548b.ps.gz