Family Sharing

To my knowledge Family Sharing doesn't support Reminders.

If you open the Reminders app you can share your lists by:

1. Tapping on the list you want to share
2. Tapping the three dots on the upper right
3. Tapping "Share List"
4. Send the Invite out

You can send the invite in a Messages group chat or a group email to prevent sending the invite out individually.

When creating a reminder you can set the date it's due, the time it's due, and how often it repeats. Make sure to create the reminder under the list you shared and set that information. Once created your husband should get a notification, you will as well, that it's due.