Best way to Embed a website into our domain

Okay we have an issue where we are using someone else website to power a portion of our website. Currently we are using an iFrame to embed their website into our website, so our visitors 'Think' they are staying on our website and everything is coming from our website. I don't think this is the best method and looking for another solution. We would like it to look like this "[login to view URL]" and this would display all information on for example "[login to view URL]". I would also like for 'Search Engine Purposes' to somehow make the search engine believe that this is 100% our information, displayed from our website. Can you set this up for us? Do you need access to our website, or the other websites that information/service we will be using, Will you be using DNS to make this happen or something else?