A person who's unbelieving denies or doubts the truth of something. Your religious grandmother might invite her unbelieving friend to come with her to church.
Being unbelieving often has to do with a lack of religious beliefs. Another way to be unbelieving is to be incredulous, or astonished by something — so amazed that you can't believe what you're seeing or experiencing. The best part about performing magic tricks for little kids is the unbelieving expressions on their faces when they see a rabbit appear in a hat or a bouquet of flowers suddenly vanish.