Proxy flavour name

I want to create a proxy server that can serve web pages such that all inner links will pass through the proxy again. any idea how such a proxy flavour is called?and if there are any open-source projects in the field?

aka user contacts a.com which then calls b.com and returns the result to the user. when a user clicks a link in the resulting page it will go to a.com (which than will repeat the process and return a page at b.com) this of course requires preprocessing js and HTML files served from b.com before serving them to the user.

I understand a perfect solution is not possible in this case, I am looking for adequate :)