Hello adamdunko,
Thank you for using Apple Support Communities! I understand that you're not getting notifications when changes are made to a shared note, however your husband receives a notification when you make changes to the note. Checking settings for the Notes app under Notifications was a great place to start. I would be happy to help provide steps to take next.
With the shared note open on your device, I'd like to have you ensure that Hide Alerts isn't turned on:
Share your notes on your iPhone, iPad, iPod touch, or Mac - Apple Support
"When a shared note is updated, everyone on the note will receive a notification that an update was made. To hide these notifications, from the note, tap
and turn on Hide Alerts."
From Settings > Passwords & Accounts > Fetch New Data, I'd also like to have you check if you have Fetch, Push, or Manual selected for your iCloud account. If this is set to Fetch, iCloud Notes will only fetch new data when the device is connected to power and Wi-Fi. If it's set to Manual, it will not fetch new data until the app is opened. Both settings can prevent notifications from appearing for the Notes app so consider changing this to Push.
Keep us posted with what happens after trying those steps.
Cheers!