Why can use iMessage with all of my contacts except for one

My wife and I just got new iPhones.  My wife can use iMessage all of her contacts who own iPhones, but when she sends me a message, it tries to send it using iMessage and will fail after about 10 minutes (which, as far as I understand, is what it's supposed to do) and send it as SMS.  I can use iMessage with every one of my contacts that has an iPhone except for her.  When I send her a message it defaults to SMS without even trying to use iMessage first. 

We are both on the same carrier and we both have data plans.  I can browse, both on wi-fi and 3G/LTE, on both phones.  I've tried deleting and readding each other as contacts, turning iMessage off and on for both, and signing out and signing back in for iMessage.  I even did a factory reset on my phone.  Can anyone help me figure out what the problem is?