iPhone text messages and iPads
I solved this by changing values under setting/messages/send receive.
For the iPhone enter the phone number then mark it with a check mark.
For the iPad enter your Apple ID.
My initial confusion stemmed from thinking that the Apple ID had to be used for both. It may have been that way long ago. I am not sure.
Good luck.

5/14/2016 Hi, your latest post says your husband has his phone number checked on his iPad. I have my Apple ID checked on my iPad. Also, I recommend deleting the old text messages as they might be giving false impressions. The original programmers are probably shocked that their strategy is being tested by families that have o many Apple devices!