Calls from and to my iPhone 4 I can make and receive phone calls from everyone and anyone except for my boyfriend. All it says is my call can not be completed and the same goes for him. So what's causing this?
Open Settings and go to General > Phone > Blocked. Make sure there's nobody on that list. 

Also, if there's a moon icon in the status bar, open Settings and turn off Do Not Disturb. 

Otherwise, I think both of you should call your service provider because this is most likely a problem on their end.