Can't recieve texts while talking on the phone

Not trying to get into any sort of debate but I would like to know how you came to your conclusion. My fiancé, my stepdaughter, and myself all have the iPhone 5s and we are all through Verizon. My fiancé and my stepdaughter are on able to send or receive any messages while on the phone or do anything else requiring data while talking on the phone. I have the same phone and same service as they do but yet while I am talking on the phone I can send and receive SMS messages and iMessages and I can also Play games requiring data, get on social media, and surf the Internet all while talking on the phone with no interruption. Given that fact I don't see how we can be an issue with the carrier

Forgive me for asking, but are you sure they are text messages instead of iMessages? iMessages has a blue bubble for the out going while text has a green bubble for out going.

Text messages doesn't use the data part of your cellular carrier. However, iMessages does use the data. With that being said, if you are on a carrier that uses CDMA like Verizon Wireless in the US. Your phone can not receive iMessage while you are on a call, because it uses data. And CDMA phones can not use data at the same time on a phone call.

KOT

If the person sending the iMessage doesn't have Send as SMS enabled in Settings>Messages, they won't switch over.

I'm having the same issue. I am on verizon. I've tested it with my my roommate, so I know for certain the settings are correct and it's not switching over to SMS automatically like it's supposed to. Then, once I'm off the call they all drop in as iMessages. I've even gone in and reset my network settings thinking that might help.

I just purchased the 5s and I have the same exact problem. I noticed it because I was on the phone with my boyfriend who was at home and I heard my iMessage ding from my iPad, but it didn't come to my phone until after we had hung up. Luckily I was talking to him so he read it to me, it was time sensitive. If I had been talking to anyone else not sitting next to my iPad I wouldn't have even realized and there would have been an issue. Have you found a fix to this?? It was never a problem with iPhone 4. I also double checked all my settings and did the reset and hard reboot.

I am having the same issue. I have the iphone 5. This has been driving me crazy for months now. I don't recall when it started but it has been a couple of months at least. I used to receive texts when on a call and I could lift the phone and read them, now, I hang up and texts will come in and sometimes, it is many texts (20 at a time) that come in all at once when I hang up. I also use Verizon. This is quite annoying.

Thank you for that info. I have verizon and I'm the only one with this problem in my group. They all have other provider.