Obviously I have no idea what you have tried or what BT have tried to resolve this so you may have tried the following already.
When he changed his password after getting the email, did he log onto his email account or click on a link within the email in order to change the password.?
What happened when he tried to change it?
What device did he use to change it?
When you set up his email account did you "gift" it to him and did he set up his own BTID?
See link how that is done.
Creating BT Email addresses? | BT Help
If you did not do the above, the email account should be linked to the BT Broadband account holder's email accounts, which in this case I assume is you. Did you previously see the email account in your BT email products in your MyBT?
If it is part of your email products try the following:-
Use only one device so make sure to turn off any other devices that he uses to access his email account.
Using a web browser, not an email client or app delete the history and cookies from the browser and then try logging onto his email account using the following link
BTMail
Assuming it won't let you log on when you do that, what happens, what message do you get?
Use the "forgot log on details". After any captcha enter his email address and click next.
What happens?
You should get a message to send a PIN to your previously chosen mobile number.
If you have not set that up you need to log into your MyBT and go to your profile and in the "Contact Details" section enter a recovery email address and mobile phone number.
Once you have received the PIN number start the forgotten email log on details again.
Assuming you get a PIN, follow the prompts.
Post back what happens.
If you did "gift" the email account to your husband and he did set up his own BTID, he should follow the above process by logging onto his MyBT.
