You can add the current-menu-parent and current-menu-ancestor to the array

function nav_class_filter( $var ) {
return is_array($var) ? array_intersect($var, array('current-menu-item', 'current-menu-parent', 'current-menu-ancestor')) : '';
}
add_filter('nav_menu_css_class', 'nav_class_filter', 100, 1);