OP - YANBU.
Unless there is an emergency this is completely unacceptable and you need to tell him this in the nicest way possible (think egg shells). You should not have to turn your phone off at night, it's not practical for everyone to do so.
Ask him to put everything in an email (many emails if he needs to!!) and tell him that you will check your email first thing each day.
Is he the kind of guy who you could really talk to? Could you say to him that you are worried that he is up all night worrying about work? If you can't do this you need to speak to someone senior at work that you trust to handle this sensitively. In this climate we need to be just that bit more careful and supportive, there are a lot of people who are stressed to the point of breaking.
Countingto10 - been there done that and emails are fine - they don't wake anyone up