How do I stop my husband getting my messages on his phone

Get your own Apple ID and set up a separate user account on the computer or set it up on your own computer. This way you have a completely separate account.

If they are coming there because has iMessage setup to read your iPhone number, there is not a way short of changing the phone number. If they arrive based on an email account you have, change the password.

Do you both share the same Apple ID...yours...? If so, go to Settings>Messages>Send/Receive on your husbands phone, remove the check next to your Apple ID. That will fix things, no new Apple ID needed.