Welcome to iMore! What email service do you use? It depends on whether your email is set up through an IMAP or a POP3 server. IMAP servers keep the original email stored remotely so, ideally, when you delete the email it should delete it from all devices as soon as the other devices check for updates from the IMAP server. POP3 accounts download the original email to the device and immediately remove it from remote server.
If your email is syncing to multiple devices it's probably an IMAP account. Keep in mind, hubby will have to have his device connected to the Internet and his email app will have to check for updates, otherwise he may still see whatever email you don't want him to see. Good luck!