Instead of overriding OnDrawItem you need to override OnCtlColor like this:
HBRUSH CMyComboBox::OnCtlColor(CDC* pDC, CWnd* pWnd, UINT nCtlColor)
{
if (nCtlColor == CTLCOLOR_LISTBOX)
pDC->SetBkColor(RGB(255, 0, 0));
return CComboBox::OnCtlColor(pDC, pWnd, nCtlColor);
}