Somebody I know got into a big fight with there girlfriend because she cheated on him. If someone is in your home and you tell them to get out and they are punching you in the face, Is it illegal to forcefully push them out of your home?

Generally, yes. Use of force is justified in self-defense. Laws may vary somewhat depending on the state or country in which you are located, so one should review the statute in your jurisdiction as well as the particular circumstances involved.

But if there are no other witnesses, her version of what happened is likely to be different than yours. You could end up being charged with assault, in which case it's a matter of her word against yours. Thus it's a good idea to refrain from using force if at all possible. Additionally, if you were brought up properly, you were taught never to hit a woman. A judge is not likely to listen to you when you argue that you didn't hit her, you only "pushed" her.

In short, I would predict that your "friend" is likely to be convicted.