I'm having a few problems with iMessages recently.
1. I can only send text messages to certain people, even though we both have iPhones are are both connected to 3G or LTE. But I can send iMessages to most people.
2. I'm not getting all messages people send me.
3, People are not receiving all of my messages. They even sometimes get just half of a message.
This has been going on for almost a week and friends with Verizon say they've been having similar issues.
What you must realize iMessage is through Apple Inc. not verizon. Verizon has the regular text sending and receiving responsibility . First thing I would say is make sure IMessage is set to "ON" on both iPhones. if it is then its Apple that has the service down and I am sure they are aware of it and fixing it.
I'm having text message problems too. In the aforementioned texts that should be iMessages, most of the text is not going through. Like the recipient is only getting the last word or even the last letter of the text. Since these are text messages, regardless of what they're supposed to be, I assume this is a Verizon problem.
The iMessage problem is going to be referred to Apple when you call tech support from another phone to have them try and fix your issue.
However I would try this first. Turn off iMessage in your iPhone settings. Leave it off and then try and send your text messages again.
If they arrive at your friends phones intact then you know it's the iMessage settings that are messing up your text messages.
If the problem persists you may have to contact an Apple store for service. Try looking for the same problem you are having at http://www.apple.com and click on support and forums.byou may get a better answer on there.