I have an ASP.NET MVC application where the default page should be index.html which is an actual file on disk.
I can browse to the file using www.mydomain.com/index.
I suspect you added index.html yourself as that extension would be unknown to the mvc framework.
Your default index page in mvc is //domain/home/index and is physically index.aspx.
If you call your domain using //domain then the routing engine will assume /home/index.aspx and not index.html.