It depends on what you think cheating is, everyone has their own view of what they consider cheating and what they don't.
But being honest, I don't think it's normal and respectful, I would consider it cheating because it's MY way of thinking.
Get rid of that girl and find someone who respects you and doesn't do that kind of thing.
You deserve someone who loves you, not someone who doesn't care about having you by their side.