What I did in the past was to register ".html" pages to be interpreted as dynamic pages, too. (I.e. just like ASPX).
This can be done through your "web.config" file:
....
<system.web>
<compilation ...>
<buildProviders>
<add extension=".html"
type="System.Web.Compilation.PageBuildProvider" />
</buildProviders>
....
and
....
<system.webServer>
<handlers>
<remove name="WebServiceHandlerFactory-Integrated" />
<add name="PageHandlerFactory-Integrated-HTML" path="*.html"
verb="GET,HEAD,POST,DEBUG" type="System.Web.UI.PageHandlerFactory"
resourceType="Unspecified" preCondition="integratedMode" />
</handlers>
....
As Robert points out, this works well with IIS 7 and IIS 7.5 (and probably on above versions, too). If you are using IIS 6, you have to do it through the IIS Management Console.