I understand you asked for a regex, but this kinda looks like XML, so here's an XML::Twig parser solution:

use strict;
use warnings;
use Data::Dumper;
use XML::Twig;

my $xfile = <<EOF;
<foo>
<item><i>headline 1</i></item>
        <item><i>headline2</i></item>
</foo>
EOF

my $t = new XML::Twig();
$t->parse($xfile);
my @x;
for my $item ($t->root()->children('item')) {
    push @x, $item->first_child('i')->text();
}

print Dumper(\@x);

__END__

$VAR1 = [
          'headline 1',
          'headline2'
        ];
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