OP, he sounds as if he needs to be hospitalised. As a former sufferer of a (severe) eating disorder myself, I can tell you that it is extremely difficult to love anyone else in the way that they deserve to be loved, and that includes partners and I would imagine children, too.
I understand that you're trying to keep him from being hospitalised and you are pouring all you have into him - until he WANTS to get better it will never be enough and you will remain the enemy, while he allows this other girl to actually communicate with him because, in a sense, she is him. I've seen a lot of eating disordered friendships, and they almost always break down if one of the friends manages to make strides towards recovery, because these friendships exist through simply mirroring each other and essentially wallowing together - or at least the majority of them.
My point being: your DP is very sick and cannot be a proper partner or parent while he is in this state. At that weight, he will be so undernourished that he won't be thinking straight and willl behave very badly. Please don't let him look after your child alone - the risk of hi passing out is real, and you don't want that.
I know I sound very doom and gloom. If your DP can begin to recover, that would be great, but it sounds like the current situation isn't working, particularly as the arrival of your DD makes it more time critical. I imagine he is getting a good deal of therapy and seeing a nutritionist but would advocate an inpatient approach, at least for a while ...
Hope I haven't overstepped my boundaries there.