Yes, if you agree, you can each claim one child. In this situation, don't even list the other child on your return, and answer "no" to the questions about custody for the child you are claiming (there is no agreement, the other parent won't claim them). (It refers to a legal order involving parents who are separated or divorced, not to an informal agreement between partners living together.)
Turbotax thinks it would be offensive to ask "are you shacking up with the other parent", so the interview is geared toward separated parents who share custody and can lead to confusion when unmarried parents live together and share custody.
