The pictures of barges on the river usually shown here are somewhat misleading , since the barges shown are fully loaded (for obvious economical reasons and since there aren't any big waves in the rivers).
However the typical hull dimentions of a barge are above 3 meter high ,
(See the link :
http://www.barges.us/bargedrafttable.html)
therefore if it's only ~ 50% filled it'll be :
a) 1.5-2 meters above the waterline. (Reasonably close to the landing craft used on D- Day)
b) Have a significant spare buyoncy for the intake of occasional wave that crosses its gunwale.
(Again - I think there were better ways to make the Sealion work than the barge fleet, but let's not get too nasty on the good old barges...)