When talking about things related to Vikings and the Swedish iron age a bearded axe would look rather like this one. I don't know what the longobards used, but it seems plausible to me that their "long bearded" axes would be closer to this form than early halberds.
(This particular axehead was found on Gotland, and is dated to the Vendel period. For full details see
http://mis.historiska.se/mis/sok/bild.asp?uid=224116 )