Today, let me explain about how to Authenticate HTML files with ASP.NET MVC. To Check Html URL is Authenticated or Not Using Asp.net/MVC using the following code:
Coding:
if (Request.RawUrl.ToLower().EndsWith(".html")) 
{ 
if (Request.Cookies[".ASPXAUTH"] != null) 
{ 
  string value = Request.Cookies[".ASPXAUTH"].Value; 
  if (value == null || value == "") 
  { 
     Response.Redirect("~/Account/LogOn"); 
  } 
} 
else 
{ 
  Response.Redirect("~/Account/LogOn"); 
} 
}

The .ASPXAUTH is the Form Authentication Cookies and Account is the Controller. The LogOn is the action. Next step, write the following code in webconfig section:
<buildProviders> 
<add extension=".html" type="System.Web.Compilation.PageBuildProvider" /> 
<add extension=".htm" type="System.Web.Compilation.PageBuildProvider" /> 
</buildProviders> 

<handlers> 
<add name="HTML" path="*.html" verb="GET, HEAD, POST, DEBUG" type="System.Web.UI.PageHandlerFactory" resourceT
ype="Unspecified" requireAccess="Script" /> 
<add name="HTM" path="*.htm" verb="GET, HEAD, POST, DEBUG" type="System.Web.UI.PageHandlerFactory" resourceTyp
e="Unspecified" requireAccess="Script" /> 
</handlers>  

I hope it works for you! Happy coding.

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