However, last night after he accepts that we are not saved by faith alone the topic of infantile baptism came up. He said that all babies go to heaven. I remember that we were taught that unbaptized babies go to purgatory. He disagrees. Can anyone give me a quick answer on baptism?
Babies are born into a state of original sin and must be baptized to be saved. This is the normative way; it is Christ's command. Unbaptized babies don't merit Heaven in any normative way because Christ said we must be baptized (born again of water and Spirit) -- but babies also don't merit punishment because they've not committed personal sin. So what happens to them? We can't say for certain. But we know this much:
Unbaptized babies don't go to Purgatory, as they can't possibly be guilty of any personal sins whose effects they need to be purged of. Purgatory is the place where already saved souls go to be purged of the temporal effects of their sins.
It is theorized that there exists a realm of the dead called "Limbo" -- a state of perfect natural happiness, like Eden before the Fall -- and that this is where the unbaptized go who are not guilty of any personal sin.
It is also possible for God to save unbaptized babies using extraordinary means of Baptism, in a supernatural way (besides which, we are bound by the Sacraments; HE isn't). But we can't presume this to be the case and we can't ignore what Jesus said. We can only know and teach as fact what we definitely know.
And what we DO know is that we have to do what Christ commands (e.g., to be baptized) -- and to trust Him in His PERFECT Justice and Mercy to deal, in the way He deems fit, with the unbaptized who are innocent of personal sin.
Sounds like you're doing a LOT of good with your friend! Yay!