Whilst DAB is less prone to multipath distortion than FM, when the signal deteriorates it first turns into a "bubbling mud" and then disappears altogether. The Jazz's bee sting aerial isn't going to be a good match to the DAB frequencies (which are about double those of the VHF FM band). Fitting an aerial specifically designed for DAB will improve reception enormously.
On a related matter, the GE Jazz's radio aerial gives exceedingly poor reception on medium wave, and the AM section of the stock radio is low bandwidth, resulting in a very muffled sound.