The iPhone allows you to say that calls from certain contacts can get through when the phone is in Do Not Disturb mode. In my experiments it seems that it's not possible to allow text messages to get through as well. Is this true, or is there some setting that I am missing?
AFIK the Do Not Disturb does not have setting to let Text Messages through like phone calls.
You can join the large group asking Apple to do it http://www.apple.com/feedback/
Edit the contact, and when you go to pick the text tone there is an option to bypass dnd.
This is done by enabling the Text Tone Emergency Bypass