When I try to open Outlook on my husband’s Windows 8 computer it says “Access denied” even though we are both administrators on the computer. I need to email customer invoices from his computer as our business is in his computer.
How did you attempt to open your husbands Outlook? Did you log in using his user?
If you just tried to open his Outlook identity respectively the PST file while being logged in with your own user then I would say that's normal.
Belonging to the administrator group simply means that your user is allowed to execute/perform certain tasks as an administrator but outside of that you are still restricted by normal users permissions.
You could try to run Outlook via "run as administrator" and open his PST file but that doesn't solve your actual problem: You would only have access to his stored emails, you won't be able to receive new ones and you won't be able to send emails from his accounts.
Account configurations are stored within the users registry. Without logging into his user account you will not be able to fully use his email account.
press Windows key to Start screen, then type outlook.exe /safe
see if this will help, other locate outlook;exe, right click on it and choose properties then under security give the rights to everyone