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Once in IIS, right click your website node and then select properties.
Find the tab at the top that says 'home directory', then 'configuration' near the bottom/right.
Once there, you'll see a list of file extensions and the 'executable path' pointing to ASP, Coldfusion etc or whatever is processing the file.
If you click 'add', then in the 'executable' field copy what it said for coldfusion files and then add ".html" as the file extension, you should be all set.