You may also be interested in HTML::TreeBuilder. Consider:

use warnings;
use strict;
use HTML::TreeBuilder;

my $html = <<'HTML';
<a href="URL1"> text1.0 <img src="SRC1"> text1.1 <br>
                <garbage2> text1.2
   <a href="URL2"> text2.0 <img src="SRC2"> text2.1 <br> <garbage2>
                   <garbage3> text2.2
      <a href="URL3"> text3.0 <img src="SRC3"> text3.1 <br> <garbage3>
            text3.2 <x1 a="a" b="b"> text3.3
      </a>
      text2.3 <haha>
   </a>
   text1.3 <oho>
   <a href="URL4"> text4.0 <img src="SRC4"> text4.1 <br> <garbage4>
                    text4.2 <x1 a="a" b="b"> text4.3
   </a>
   text1.4
</a>
HTML

my $tree = HTML::TreeBuilder->new_from_content ($html);

for my $elt ($tree->look_down ('_tag', 'a')) {
    print "A " . $elt->attr ('href') . "\n\tTEXT: '";
    
    my @text_segs;
    
    for my $child ($elt->content_list ()) {
        next if ref $child and $child->{_tag} ne 'a';
        last if ref $child;
        push @text_segs, $child;
    }
    
    print "$_ " for @text_segs;
    print "\n";
}
[download]

Prints:

A URL1
    TEXT: ' text1.0   text1.1    text1.2  
A URL2
    TEXT: ' text2.0   text2.1     text2.2  
A URL3
    TEXT: ' text3.0   text3.1    text3.2  text3.3  
A URL4
    TEXT: ' text4.0   text4.1    text4.2  text4.3
[download]