You should modify drilldown structure and add id for each "interior" serie, and parentID for "outer" serie. Then use get function (http://api.highcharts.com/highcharts#Chart.get()) to display "parent" name.
It is simple example which display name for MSIE, but if you add all parameter for other series, then it will work for each of them.
point: {
events: {
click: function (event) {
var parentSerie = this.options.parentId;
alert(this.series.chart.get(parentSerie).name);
}
}
}