I ran into trouble with the Parched's ajaxComplete approach, in consistently and generally providing it with the proper target to apply the behavior to (e.g. AFAICT xhr.responseText isn't a part of the document, so it can't be bound to), so I came up with this alternate approach, which may be helpful.
In all my ajax calls I use the complete: event to trigger a known event on the new html's destination.  E.g. the facebox container or the pjax destination.
// in my facebox ajax setup
$.ajax({
  ...,
  complete: function() {
    $('#facebox').trigger('end.facebox');
  }
}
Then separately I react to this event.
$('*').live('end.facebox', function(e) {
  if (e.target == this) {
    apply_behavior(this); // in the style of Parched Squid's myInitialize
  }
});
I'd love to hear suggestions/improvements, but this seems general enough to consistently accommodate multiple ajax approaches/event types and destinations.