I think this song is about a woman who is denying that the speaker is the father. However, the speaker knows that the baby is his, and he wants caroline to tell him the truth. "baby's eyes look just like mine, we've both been through it, tell the truth for once just this time".
It's evident that caroline's not going to let the speaker see the child, and because of this, the child's life will be scarred in the way that she will never know who her real father is. Caroline wants to protect herself and keep away from the father, but this would only be hurting their child. "When you teach this little girl to walk, another will remind, there's a price to pay for a place safe to hid from inside" (the 'another' is the child-i think). that's all i got for now :)
This song seems to be about a man who has been through so much with the woman he loves, and is at the point where he is just fed up with their relationship. Caroline and the guy (Stephan?) have obviously been through a lot together -- "Knowing we've been through it"-- and he just wants her to "tell the truth for once just this time."
It's kind of unclear, but it seems like she has a baby girl that is his, but she wont tell him truthfully if it is or not. He seems to know she is his daughter-- "Baby's eyes look just like mine"-- and even if the child was a mistake--"Didnt know what we made laying down"-- he just wants Caroline to tell him the truth. ALL he wants is the TRUTH!!!
The most prevalent feeling from this song is that he is just FED UP and kind of giving in to Caroline-- all that he wants from her is the truth, after all they went through. He is really giving in to her; he doesnt want to fight anymore-- "So ALRIGHT, Caroline." When he says, "I wont take nothing from you...Even if it means the truth", I interpreted that as him knowing that she is not telling him the truth, and him finally giving up and not pushing for it anymore.