It really depends.  IF you pass the interview, you will still need to be sworn in and that ceremony can take place anywhere from 1-3 or so months after the interview.  You are NOT a US citizen until after you are sworn in so you cannot claim to be a US citizen or try to apply for a US passport until that time.  If you have to travel before you are sworn in, you will need to do it just like you have been doing it beforehand--with a green card and any visas you may need to get to enter countries.