Hi Maggieinthemoment,
You can confirm that the Family Sharing settings are enabled correctly to grant your husband access to the Apple Music subscription, however, it does sound like the device may be experiencing some connection issues.
On both your device and his, confirm that Purchase Sharing is enabled.
- Go to Settings > Your Name
- Tap on Family Sharing
- Tap Purchase Sharing and confirm Share purchases with Family is enabled
If you can't find your family's shared content - Apple Support
If enabled, you can troubleshoot the connection on your husbands device.
- Close the Music app out completely. Closing the app and relaunching it can help when experiencing unexpected behaviors. Check out how to close an app here: Close an app on your iPhone or iPod touch - Apple Support.
- Restart his iPhone. Restarting can help refresh the connection and process. Check out: Restart your iPhone - Apple Support
- Install any iOS updates that may be available. The Music app updates as part of the iOS. Updates contain many bug fixes that can help your device to function as expected. Check out: Update your iPhone or iPad - Apple Support.
Have a good one!