My wife and I both have iPhones. When I text her, it shows up in green, not blue.?

I don't know how much you know, so I'm sorry if it seems belittling, but here's my answer. The blue colour is the colour of iMessages, green is normal texts. iMessage uses the Internet and is between iPhones, which means you need an Internet connection, wether it be your mobile data or wifi. For these to send you need to have iMessage turned on. This is under messages in settings. Also you could go to your wife's number in the contacts and select edit. Here you can change 'mobile' to 'iPhone', although I don't think that makes a difference

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Do you both have iMessage enabled? Go to Settings > Messages and enable iMessage

Also make sure you both have some kind of internet connection, whether it be WiFi or 3G/4G, iMessage uses internet connection to send messages, what you're sending are SMS messages.

Check the iMessage settings for both phones (particularly hers) & ensure everything is set up properly

Not sure. Is it suppose to be green? Ask the agent you bought the phone off of.