In general, you can't reliably parse entire HTML or XML documents with a single regex.
You CAN, however, parse individual bits of wellformed XML out of a string using a regex. For example, you can have a regex that correctly matches a single empty element (though it won't parse individual attributes, just recognize that there are zero or more of them.) Or you can have a regex that will match an element. Or you can have a regex that matches a non-empty element that contains only text.
By combining several such regular expressions in a small number of simple functions, some of which are directly or indirectly recursive, I believe it is possible to parse well-formed XHTML in a couple of screens full of reasonably maintainable Perl code. If I'm wrong, it would be because XML allows something I'm not aware of and never use (e.g., if there were some kind of non-trivial quoting mechanism for embedding non-entity-ized quotation marks in attribute values, that could really gum up the works).