Remember that the purpose of HTMLParser is to let you build a document tree from an input. If you don't care at all about the document's structure, then the str.join solution @falsetru gives will be fine. You can be certain that all element tags and comments will be filtered out.
However, if you do need the structure for more complex scenarios then you have to build a document tree. The handle_starttag and handle_endtag methods are here for this.
First we need a basic tree that can hold some information.
class Element:
    def __init__(self, parent, tag, attrs=None):
        self.parent = parent
        self.tag = tag
        self.children = []
        self.attrs = attrs or []
        self.data = ''
Now you need to make the HTMLParser make a new node on every handle_starttag and move up the tree on every handle_endtag. We also pass the parsed data to the current node instead of holding it in the parser.
class MyHTMLParser(HTMLParser):
    def __init__(self):
        super().__init__()
        self.root = Element(NONE, '__DOCROOT__') # Special root node for us
        self.current = self.root
    def handle_starttag(self, tag, attrs):
        newel = Element(self.current tag, attrs)
        self.current.children.append(newel)
        self.current = newel
    def handle_endtag(self, tag):
        self.current = self.current.parent
    def handle_data(self, data):
        self.current.data += data
    def handle_charref(self, ref): # No changes here
        self.handle_entityref('#' + ref)
    def handle_entityref(self, ref): # No changes here either
        self.handle_data(self.unescape("&%s" % ref))
Now you can access the tree on MyHTMLParser.root to get the data from any element as you like. For example
n = '<strong>I <3s U & you luvz me</strong>'
p = MyHTMLParser()
p.feed(n)
p.close()
def print_tree(node, indent=0):
    print('    ' * indent + node.tag)
    print('    ' * indent + '  ' + node.data)
    for c in node.children:
        print_tree(c, indent + 1)
print_tree(p.root)
This will give you
__DOCROOT__
    strong
      I <3s U & you luvz me
If instead you parsed n = <html><head><title>Test</title></head><body><h1>I <3s U & you luvz me</h1></body></html> You would get.
__DOCROOT__
    html
        head
            title
              Test
        body
            h1
              I <3s U & you luvz me
Next up is to make the tree building robust and handle cases like mismatched or implicit endtags. You will also want to add some nice find('tag') like methods on Element for traversing the tree. Do it well enough and you'll have made the next BeautifulSoup.