You did ask for a solution that will work with Chrome and Firefox as well, that means automation of the web browser. Which Mike is referring to.
MHTML is not the same as HTML. It's a local version of whatever the web browser thinks will be required. That means that if the server sends different content for different browsers then that's what will happen. Some variation is routine, although now IE6
is dying off that's no longer as big an issue as it once was.
Which also means that you can't ensure it's a browser non-specific version that's being saved. If you want/need a copy of the HTML being rendered by Chrome/Firefox then you'll need to find a way to script/automate those browsers and I don't know of one either.