(I ask my question again after the first one was terribly formulated)
I face the following problem:
Here's a way to do it for Firefox, Opera, Chrome and Safari. Basically, you just do div.innerHTML = div.innerHTML to reinterpret its content as HTML, which will make that class attribute from the XML file be treated as an HTML class name.
Remove the this.status === 200 if you're testing locally in browsers that support xhr locally.
The importNode() function doesn't seem to work in IE (9 for example). I get a vague "interface not supported" error.
You could also do it this way:
var doc = this.responseXML;
var markup = (new XMLSerializer()).serializeToString(doc.getElementsByTagName("response")[0].getElementsByTagName("div")[0]);
div.innerHTML = markup;
as long as the markup is HTML-friendly as far as end tags for empty elements are concerned.