How about asking him what his morning routine is like with her? Ask him what time she is waking up for him, has her diaper changed, etc. You could even make up a little log book page, and just tell him that since things are a little different between the two households, you wanted to write down her schedule for each house so you don't get too confused.
In other words, put it on you. Hopefully, that will give you an opening to say something about what her schedule usually is. Also, if he's new to this, there's a good chance things will improve as he gets better at remembering the routine and reading her signals.
This is difficult, because you obviously can't tell MB without opening a huge can of worms, but that poor kid!