Can I allow text messages from certain contact through when in Do Not Disturb mode?

Solution 1:

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/

Solution 2:

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