Hosting WPF app inside non-WPF app using WIn32 SetParent()

I have a WPF application that I want to look like it is hosted inside another - non-WPF - application. In real life this non-WPF app is an ActiveX inside Internet Explorer, but for the sake of illustrating the problem I use a simple Windows Forms app.

I use the Windows API function SetParent, which there are dozens of threads on already. However, I cannot find anything written on my exact problem: A small region on the right and bottom of the WPF app is not painted inside the non-WPF app's window.

The WPF window running by itself:

The WPF window with WinForm app's window as parent:

I don't experience the problem if a swap the WPF app with a WinForms app or a plain Win32 app (like Notepad).

The WinForm code looks like this:

private void Form1_Load(object sender, EventArgs e)
    {
        // Start process
        var psi = new ProcessStartInfo("c:\\wpfapp\\wpfapp\\bin\\Debug\\wpfapp.exe");
        psi.WindowStyle = ProcessWindowStyle.Normal;
        _process = Process.Start(psi);

        // Sleep until new process is ready
        Thread.Sleep(1000);

        // Set new process's parent to this window
        SetParent(_process.MainWindowHandle, this.Handle);

        // Remove WS_POPUP and add WS_CHILD window style to child window
        const int GWL_STYLE = -16;
        const long WS_POPUP = 0x80000000;
        const long WS_CHILD = 0x40000000;
        long style = GetWindowLong(_process.MainWindowHandle, GWL_STYLE);
        style = (style & ~(WS_POPUP)) | WS_CHILD;
        SetWindowLong(_process.MainWindowHandle, GWL_STYLE, style);

        // Move and resize child window to fit into parent's
        MoveWindow(_process.MainWindowHandle, 0, 0, this.Width, this.Height, true);
    }

Note: I'm aware that this use of SetParent is not necessarily a recomm