One of my pet peeves is that sometimes the talents of my band get overlooked because, and it was the same problem that Frank Zappa had, with a lot of groups that use humor, people don't realize there's a lot of craft behind the comedy.

This quote is referring to a common problem that many bands who use humour in their songs face: people often don’t recognize how much skill and effort go into making the music. Frank Zappa, a famous musician, also faced this issue: though his songs often had a comedic element, the skill and effort put into them was often not appreciated. The speaker is saying that this problem can be a pet peeve of theirs and that it’s a problem similar to what Frank Zappa experienced.