op - does it have to be 48 hours? would you consider 24 (or in fact less but still overnight iyswim)I have to say I agree with More that men are just as capable (obv. apart from not having boobs). However I also agree with others that, in your circumstances, your ex may not be quite as capable - not because he's a man though, but simply because he won't have had the 4 weeks that you've had to learn all about her, to stare, and soak in every little (lovely)detail. but that, in fact, could be an argument for letting him do this - the sheer intensity of looking after such a little one is something that, imo, helps our love for them (whether we are male or female) cement and grow. which can only be a good thing.
Apart from his abilitites the other difficulty everyone's been pointing out, is breast-feeding and expressing. and here, at 4 weeks, I agree that 48 hours might be difficult (but every woman and every baby is different, so it's very hard to generalise). depending on how feeding and expressing is going could you suggest that his first overnight is in fact 12-ish hours and not 48? in actual fact if he's been having her for the day, in terms of time, that would actually be a gradual step.
things must be very difficult for you now but if you and ex can work together imo it will have great benefits in the long-term. if you can talk this through, see each other's pov, make sure you both have dd's interests at heart, you should be able to come up with a plan that suits everyone as best as possible in the circumstances.
and finally - all of the above could be batted away if, in fact, your ex is, just an irredeemable arse. but perhaps he's not.
good luck - and congrats on your newborn. enjoy her.