Just used this logic on a triple hash! Works beautifully!

for my $key1 (sort keys %linehash) {
    $outSect1 =  $key1;
    for my $key2 (sort keys %{$linehash{$key1}}) {
        $outSect2 = "$outSect1.$key2";
        print "$outSect2\n";
        for my $key3 (sort keys %{$linehash{$key1}{$key2}}) {
           if ($key3 ne ""){

              print "\t", $key3, " = ", $linehash{$key1}{$key2}{$key3}
+, "\n";
             }
           }
    }
}
[download]

Your humble servant,
-Chuck