The user would click on a link to go to the herbal supplement site and buy the product there. Then he would click on a different link to go to the aromatherapy product site and buy it from there.
I suspect that you're thinking of having some sort of shopping cart on your site where the user would put both items in the cart and checkout once. Not going to happen. Like jimbeetle said, as an affiliate, you're not directly involved in the ordering part.
The only affiliate programs that I am aware of that allow affiliates to handle any part of the order process are hotel reservations sites doing a private label implementation.