How to stop husband's iPhone pictures from going to my Apple desktop?

It appears that your husband's iPhone and your Mac is sharing the same Apple ID account. This is causing the photos to sync from your husband's iPhone to your Mac.

You can either stop sharing the same Apple ID by logging in your Mac with your own Apple ID

OR

On your Mac, you can open the Photos app ➡️ Photos (top left) ➡️ Settings ➡️ iCloud tab ➡️ iCloud Photos: Ensure that this setting is unchecked (no check mark).

Axel F.

Stop sharing an Apple ID.

Each person should use their own Apple ID, and many things will get merged and combined when one is shared, such as photos.

Make sure you are logged in to your own Apple ID in System Preferences ➡️ iCloud / Apple ID.