wordpress with in our php site

We are going to put our multi-site users Wordpress back end within the frame work of our secure back office so they have easy access to their blog and we wish to auto log them into the their multisite when logged into our secure site so its not a double login process.

The issue is that their username and password for our site and their Wordpress multisite is not the same as we have two separate DB's. Can you recommend anything so our past, present and future members can have identical usernames and passwords? (so they can be auto logged into Wordpress while in the secure back office on our php site)