some apps are asking me for my husbands password for his email instead of mine

All apps are forever tied to the Apple ID used to download them.

Apps from one Apple ID cannot be merged or transferred to another Apple ID.

You have to delete those apps from your husband and download them using your own Apple ID

or ask your husband to setup family sharing with you, click and read below:

Family Sharing - Apple Support

iTunes begs to differ.

I seem to remember putting his email in somewhere as a backup of sorts in case something happened to my email address but can't find that now either

It seems you may restored from one of his backups. iTunes purchase history, but not the apps themselves are stored in a backup.

iTunes is detecting those apps were acquired using his Apple ID.

You can either remove them and download them using your Apple ID, or start a family for Family Sharing to share iTunes purchases.

Family Sharing - Apple Support

iTunes will name each backup for the phone it came from, but if you restore from "his" backup, that could explain what is happening.

Regardless of how it happened, it happened and what we have suggested is the way you solve it.

Or go back to the computer and see if there is a recent backup for "your" phone and restore it.