Can XDomainRequest be made to work with SSL?

I have code that uses Microsoft's XDomainRequest object in IE8. The code looks like this:

var url = "http://<host>/api/acquire?<query string>";  
var xdr = new XDomainRequest();  
xdr.onload = function(){  
    $.("#identifier").text(xdr.responseText);  
};  
xdr.open("GET", url);  
xdr.send();  

When the scheme in "url" is "http://" the command works fine. However, when the scheme is "https://" IE8 gives me an "Access denied" JavaScript error. Both schemes work fine in FF 3.6.3, where I am, of course, using XmlHttpRequest. With both browsers I am complying with W3C Access Control. "http://" works cross origin for both browsers. So the problem is with IE8, XDomainRequest, and SSL.

The SSL certificate is not the problem. If I type https://<host>/ into the address bar of IE8, where <host> is the same as in "url" above, the page loads fine.

So we have the following:
- hitting https://<host>/ directly from the browser works fine;
- hitting https://<host>/api/acquire?<query string> via XDomainRequest is not allowed.

Can it be done? Am I leaving something out?