Try replacing your while loop with something like this (untested):

my @dircontents = readdir(DIRHANDLE);
my @dirs = grep { -d $_ && $_ !~ /^\.\.?$/ } @dircontents;
my @files = grep { -f $_ } @dircontents;

print "<B>$_</B><BR>\n" foreach (@dirs);
print "$_<BR>\n" foreach (@files);
[download]

That can, of course, be golfed down quite a bit but hopefully it's pretty clear what's going on.