Member within two Access Levels/Subscriptions


I have the following case.

I use a login via Facebook and asign the user a free membership, which gives him access to some sites, but restricts the access to Site "paid Site".

Then if he signs up for the subscription "Paid Subscription" he is then member of both free and paid subscription.
Now my problem. He has then no access to the "paid Site" because his membership in "free member" does not allow him to access the site.
"free member" and "paid member" works against each other.

How can I solve the problem, that "free member" has no access and "paid member" has access.

Thanks in advande.