Getting XML Data from Ajax Response

I'm getting the following XML response back from a Wordpress AJAX request and having trouble extracting the data. I think it's because it's being parsed as CDATA, but I can't see why.

<?xml version="1.0" encoding="UTF-8"?>
<wp_ajax>
   <response action="mz_mindbody_ajax_add_to_class_0">
      <object id="0" position="1">
     <response_data><![CDATA[error]]></response_data>
     <supplemental>
        <classID><![CDATA[2237]]></classID>
        <message><![CDATA[Error in add to class (2237)]]></message>
     </supplemental>
      </object>
   </response>
</wp_ajax>

This is the php to handle the AJAX call:

<script type='text/javascript'>
/* <![CDATA[ */
var my_parameters = {"ajaxurl":"http:\/\/localhost:8888\/wp-admin\/admin-ajax.php"};
/* ]]> */
</script>
<?php

// Ajax Handler
add_action( 'wp_ajax_my_ajax_handler', 'my_ajax_handler' );
function my_ajax_handler() {
    // Get the Post ID from the URL
    $classID = $_REQUEST['classID'];

    // Instantiate WP_Ajax_Response
    $response = new WP_Ajax_Response;

    if( wp_verify_nonce( $_REQUEST['nonce'], 'nonce-name' . $classID )){
    //Do something here

    $response->add( array(
        'data'  => 'success',
        'supplemental' => array(
        'classID' => 'did it',
        'message' => 'Class ID goes here', // ideally want to show $classID
        ),
     ) );
    } else {
    // Build the response if an error occurred
    $response->add( array(
        'data'  => 'error',
        'supplemental' => array(
        'classID' => 'nothing to see here',
        'message' => 'Error in add to class',
        ),
    ) );
    }
    // Whatever the outcome, send the Response back
    $response->send();

    // Always exit when doing Ajax
    exit();
}
//End Ajax

This is the jQuery code:

(function($){
$(document).ready(function($) {
    $( '.my_class' ).click( function( e ) {
        var link = this;
        var id   = $( link ).attr( 'data-id' );
        var nonce = $( link ).attr( 'data-nonce' );

        // This is what we are sending the server
        var data = {
            action: 'my_function',
            classID: id,
            nonce: nonce
        }
        // Change text of link
        $( link ).text( 'DOING IT' );

        // Post to the server
        $.post( my_parameters.ajaxurl, data, function( data ) {
            // Parse the XML response with jQuery
            // Get the Status
            console.log(data); //the XML data posted above
            var status = $( data ).find( 'response_data' ).text();
            // Get the Message
            var message = $( data ).find( 'supplemental message' ).text();
            // If we are successful, add the success message and remove the link
            console.log(status); // empty string
            if( status == 'success' ) {
            $( link ).parent().after( '<p><strong>' + message + '</strong></p>').remove();
            } else {
            // An error occurred, alert an error message
            alert( message );
            }
        });
        // Prevent the default behavior for the link
        e.preventDefault();
        });
    }); 
})(jQuery);

In the tutorial I'm following the $response->add() calls are within a function. Is the fact that mine aren't what's causing the problem here?

Wait - I have misrepresented the data "object", which may be part of (or all of) the problem. The entire data "object" is actually a string, which in the console looks like:

<script type='text/javascript'>
/* <![CDATA[ */
var mz_mbo_params = {"ajaxurl":"http:\/\/localhost:8888\/wp-admin\/admin-ajax.php"};
/* ]]> */
</script>
<?xml version='1.0' encoding='UTF-8' standalone='yes'?><wp_ajax><response action='mz_mindbody_ajax_add_to_class_0'><object id='0' position='1'><response_data><![CDATA[error]]></response_data><supplemental><classID><![CDATA[nothing to see here]]></classID><message><![CDATA[Error in add to class]]></message></supplemental></object></response></wp_ajax>