My husband and I watch this show with our children (teens). We've learned so much from our children about the type of peer pressure they've been exposed to, how much alcohol is in a school each day, as well as other things that were only brought up because of the mood we were in.
My daughter came home yesterday so excited because her teacher started talking about something she had seen on Drunk History, and she was able to offer up information that was not in the materials given to students. She didn't tell the teacher or her classmates where she had learned about the topic (to be respectful!), but my daughter sure was beaming when she got home from school!
The show is very educational and can help forge a love of history. I just recommend that you talk with your child(ren) for a few minutes at minimum after each episode.
If you're unsure, just watch an episode without your children.