This whole thing confuses me. I thought that if you married an american, you were allowed to live with them in the US indefinitely. Am I missing something?
You are if the paperwork gets approved after your marriage and you get permanent legal residency (as a result i.e., the vaunted green card). It's often easier for the alien to go back to her country after the marriage because it can take as little as six months to apply for and get a permanent residency visa. When you stay here after the marriage, it's a slightly tougher row to hoe because you have to convince USCIS that you didn't enter the country with the intent of getting married, that the marriage is legitimate, etc. (You always have to prove the marriage is legitimate, however.)