Accidentally deleted my husband's hard drive on old 360.

Yikes, I am so sorry to hear about you situation. The others have answered the question, but I wanted to add that going forward you could use an USB flash drive that you could use for saves. Having a backup place to save would hopefully help you manage
your storage better.

Unfortunately, if the Xbox 360 was used offline and you didn't use Cloud Saves or used an online profile, I'm afraid what you deleted is now gone forever.

In theory, you could try to hire a service specialist for data recovery like
Ontrack, but a professional data recovery service usually costs several hundreds if not thousands of US-Dollars (or equivalent of your local currency).

So usually, if it hasn't been synchronized online, everything you deleted on the 360 is now lost, I'm afraid.

Very sorry to hear that, as others have said, it seems the saves will be gone for good. This is one good improvement that was made with the Xbox One, is that it also backs up your saves to the Cloud. If your husband and you do decide to get an Xbox One
down the road, at least you won't have to worry about with that console. Sorry to hear this happened though, I hope it doesn't cause too much of a setback for you both!

Hello, that's not good.

You say "isn't hooked up to wifi and our router is Netgear" Is the Xbox connected wired?

If yes, a good chance that it saves some profile and savegames to the Cloud servers.

The saves and games would be removed, but profile and account information would still be retained. Although he wouldn't be able to pick up where he left off, you could still use the discs to install and play, as well as download purchased digital titles.
Achievement data and entitlements will still be available for the account. The real loss is the save data, and that can mean a lot, so I'm sorry for that; accidents happen.

Best of luck!