How to automate an IE webapp that pops a modal HTML dialog?

[Revised yet again for clarity]

I have a C++ program which interacts with a website. The site is IE-specific, and so is my program.

I'm connecting to the running instance of IE in an ordinary way (out of process -- see code). Once I get the IWebBrowser2, I have no problem getting the IHTMLDocument2 and interacting with the individual IHTMLElement objects, filling in fields and clicking buttons.

But if the web page has javascript that calls window.showModalDialog, I'm stuck: I need to interact with the HTML elements in the popup, just like the other pages; but I can't seem to get its IWebBrowser2.

The popup is always titled "Web Page Dialog", and is a window of type Internet Explorer_TridentDlgFrame containing an Internet Explorer_Server. But I can't get the IWebBrowser2 from the Internet Explorer_Server window the way I can when it's a normal IE instance.

I can get the IHTMLDocument2Ptr, but when I try to get the IWebBrowser2 I get an HRESULT of E_NOINTERFACE.

The code is pretty standard stuff, and works fine if it's a 'normal' IE window

IHTMLDocument2Ptr pDoc;
LRESULT lRes;

/* hWndChild is an instance of class "Internet Explorer_Server" */

UINT nMsg = ::RegisterWindowMessage( "WM_HTML_GETOBJECT" );
::SendMessageTimeout( hWndChild, nMsg, 0L, 0L, SMTO_ABORTIFHUNG, 1000, 
    (DWORD*)&lRes );

LPFNOBJECTFROMLRESULT pfObjectFromLresult = 
    (LPFNOBJECTFROMLRESULT)::GetProcAddress( hInst, "ObjectFromLresult" );
if ( pfObjectFromLresult != NULL )
{
    HRESULT hr;
    hr = (*pfObjectFromLresult)( lRes, IID_IHTMLDocument, 0, (void**)&pDoc );
    if ( SUCCEEDED(hr) ) {
        IServiceProvider *pService;
        hr = pDoc->QueryI