How do I prevent my husband’s emails from combining with my Mail.app account?
You don't specify if this is on a Mac or an iPhone etc? Also knowing what version of macOS or iOS you're running would be helpful.

However, the solution is to remove his gmail email account from your Mail app. The steps for doing this will depend on whether you're using a Mac or an iPhone etc.

EDIT

Edited answer to provide some step-by-step instructions for removing gmail accounts from Apple mail in macOS and iOS.

Steps for macOS:


Open the Mail app
Go to: Mail > Accounts...
In the Internet Accounts window that pops up you will see a list of all email addresses being used by Mail
Click on the address you no longer want
At the bottom click on the minus (-) sign to remove the account
Click OK when you are asked if you're sure
Close the Internet Accounts window


Steps for iOS:


Go to Settings > Mail > Accounts
Tap on the account you want to remove
Scroll to the bottom of the screen and tap on Delete Account
Tap Delete Account when you are asked if you're sure
Exit your settings


Hope this helps!