but if you want complex parsing you're better off using a complex parser.

Well... no. If you want correct parsing, you should use a parser. A regex like that can indeed work but it has many edge cases where it will fail and I am personally sick of inheriting code that fails when there are numerous, well-known, deeply tested and vetted ways to solve the problem correctly.

For quick one-offs or if you know your input intimately a regex on HTML can be okay but for production code it is just Wrong™. Also, I realize you might understand this and just chose poor terms but s means . matches newlines (the single line modifier), m is the multi-line modifier; perlre.