Is it permitted to quote something with informal language, like an interview excerpt with 'haha', in a thesis? One of the interview excerpt I want to quote include "haha."

Is it permitted to quote an interview excerpt with 'haha' in a thesis?

I asked because it seems like it is too informal.
You should consult with your advisor about conventions in your field.  I think generally, people lightly edit interviews such as these, so if the laughter isn't revelant to what the subject is saying, you can leave it out.  If it is important, you don't have to onomatopoetically transcribe it as "haha."  You can write 
"[laughter]" or "[interviewee laughs]."