You have two options:
Referer clearing or referer spoofing.
For referer clearing the standard method would be a double meta refresh. (Though this will lose you traffic from users on Safari and some other less common browsers, as their referers will not clear so you'll have to send them elsewhere.) Your affiliate will see no referer, which can be suspicious at times.
For spoofing you javascript redirect to a whitehat/greyhat domain. Then when you get there, you check if you just got javascript redirected (as you use it to add a POST argument.) If you did get there via javascript redirect, then send them on to the affiliate with another javascript redirect, if they didn't then just render the page as usual. Thus, it will look like theyr'e coming from a whitehat domain, possibly a page w/ a banner ad, so you look legitimate.
