We do not offer "unlimited" web space, bandwidth, and other resources as in our opinion, as it is impossible for just about any host to offer such a thing. The term "unlimited" is often used by hosts purely as a way to gain your custom. All hosts have a point where your site can take up too much hard drive space, use too much bandwidth each month or even overload the server's processor to the point where it affects the server's ability to deliver pages on other sites.
Take a close look at the host's T&Cs, and there will be a "fair use" policy there somewhere giving them a get out clause if they think you are using too much of their resources.
True "unlimited" accounts probably do exist, but they are rare and you will have to pay for it accordingly.