URL parsing is not so simple. You can write regexp for your case like this:

use strict;
use warnings;

my $str1 = 'http://hostname.company.com:80//directory/';
my $str2 = 'http://hostname.company.com:80//';

for ( $str1, $str2 ) {
    my ( $host, $dir ) = m{https?://([^:]+):\d+//(:?([^/]+)/)?};
    print "Host: $host, Dir: ", ( defined($dir) ? $dir : 'undefined' )
+, "\n";
}
[download]

But it's better to use module URI

P.S.: btw, why there are two slashes?