Parsley is not as widely-used as coriander, but yes, it is used, as well as many other herbs. I personally prefer parsley in this soup, it's a "my family thing". You can use coriander if you like it better.

The same happens with thyme, for example. In the northwest, where I come from, it's unthinkable to cook any stew or legume dish without it. My capitaleño friends had never used it.