I'm glad that you folk in the USA understand and appreciate British humour at it's best. Congratulations too, because even Britain's close neighbours in Europe often don't understand it.
Most of the Blackadder episodes were comedy skits based on British history with brilliant one liners and a tinge of serious social comment here and there. The WWI series was most definitely black humour. Under the jokes was serious criticism of the social structure of the day that sent young men to their deaths whilst their idiot wealthy leaders sat comfortably well back from the front line. A bit like some things that go on today, you might say.
If anyone would like to explore British tv sit com. humour further there are episodes from excellent old programmes on You Tube. Search for titles such as:
Last Of The Summer Wine
One Foot In The Grave
I Didn't Know You Cared
I hope you enjoy.