Conner Carey, iPhone Life, in a post from a year back:

The Do Not Disturb function on iPhone allows you to silence all incoming calls, texts, and notifications. Here’s how to bypass Do Not Disturb for individual contacts using a feature called Emergency Bypass. This allows the people designated to reach you on your iPhone even if your Do Not Disturb settings are set to silence calls and texts from everyone.

Obviously, this has been around for a while, but the discoverability is pretty low, thought it worth posting. Here’s the details:

• Go into Contacts
• Search for a contact you want to be able to reach you, even if you have Do Not Disturb enabled

(Note that “Add to Emergency Contacts” is on this page. Not what we’re going for, that’s for the Health app and emergency responders)

• Tap Edit to edit the contact
• Scroll down and tap Ringtone
• There at the top of the Ringtone page is the Emergency Bypass switch.

Emergency Bypass allows sounds and vibrations from this person even when the ring switch is set to silent, or when Do Not Disturb is on.

Since you’ve come this far, take a minute to visit:

Settings > Do Not Disturb

Note the Allow Calls From setting, which defaults to your Favorites list. Slightly different from Emergency Bypass. This is about phone calls. Odd to me that they are not integrated in some way.

No matter, thought this was worth a visit.