Affiliate Marketing Secrets

As an affiliate for a product, I want an order form on my landing page. When the buyer completes the order form, I want the buyer to be taken to the company’s own checkout page (where they select how many of the product they want… and provide their payment info.) The problem is, I want those subsequent pages (checkout page and thank you page) to have my same domain and not show the company’s domain. How is it possible to code this? Essentially, the order form which will “live” on my landing page should be coded to actually be the parent company’s order form, but will simply contain my affiliate number in the code. Does this make sense… and is it possible? Thank you!!