They could incorporate everything into the same site.  They just need to enable the ASP.NET version you are using on the existing virtual folder.  That way, they can just reference your site with relative URLs.

Otherwise, they could create an application in IIS as normal, using the ASP.NET version you used to create the pages.  In their HTML site, they can add a folder, and have it redirect the user to the ASP.NET path. 

Either way, the HTML pages could use relative or absolute URLs.  An integrated site (option 1) would be easier to maintain, since everything would physically exist under a single folder.