Using someone else's iTunes account, even when you have your own My husband and I both have iTunes accounts.
Can I sign onto his account to download some of his music.
Yes, you can listen to any of your family member's music, but not in the way you suggested. In fact, you can even use any of their purchases. To do that you need to have Family Sharing.

Go to https://support.apple.com/en-us/HT201088 to setup Family Sharing.