I'm creating a project on character traits, and the person that I'm writing about is funny yet serious. I didn't know if there was a word for that, so I'm asking for help.
Maybe here's what you are looking for -
: treating serious issues with deliberately inappropriate humor; flippant.
"a facetious remark"
For example -
Jacky was being facetious when she said, "Yes, let's all go to Iraq for my birthday party!"
Jacky is trying to sound serious while saying this, but it is not supposed to be taken seriously; it's supposed to be humorous. So basically, you can say that she is being serious and humorous at the same time.
You might call this person
Deadpan means "without emotion," but the most often-used context is "deadpan humor" which is humor delivered in a serious manner.