Simply add AJAX callbacks to your WordPress Theme

functions.php

<?php
/**
 * 1. Add this to your theme's functions.php file.
 * 2. Create an 'ajax' folder in your theme directory.
 * 3. Create a PHP file to handle the AJAX call in the ajax folder.
 * 4. From Javascript, make an AJAX call using jQuery:
 * 5. $.get( window.themeSettings.ajaxUrl, {action: window.themeSettings.themeAjaxAction, template: 'YOUR TEMPLATE NAME (MINUS THE .php EXTENSION)'}, function( data ) { } );
 */


/**
 * A generic AJAX handler for the theme
 */
function themename_themeajax_handler() {
  $template = isset($_REQUEST['template']) ? $_REQUEST['template'] : '';

  if( !empty($template) ) {
    locate_template( array('ajax/'.$template.'.php'), true );
    die();
  }
}
add_action('wp_ajax_nopriv_themeajax', 'themename_themeajax_handler');
add_action('wp_ajax_themeajax', 'themename_themeajax_handler');


/**
 * Set the content-type for the header
 *
 * @param $type string - the short reference for the type
 *
 * Accepted types: json, javascript, rss, text, xml, atom, css, html
 */
function themename_themeajax_set_type( $type ) {
  $types = array(
    'json' => 'application/json',
    'javascript' => 'text/javascript',
    'rss' => 'application/rss+xml; charset=ISO-8859-1',
    'text' => 'text/plain',
    'xml' => 'text/xml',
    'atom' => 'application/atom+xml',
    'css' => 'text/css',
    'html' => 'text/html'
  );

  if( isset($types[$type]) ) {
    header( 'Content-type: '.$types[$type] );
  }
}



function themename_themeajax_print_settings() {
  echo '<script>';
  echo 'window.themeSettings = ';
  echo json_encode(array(
    'ajaxUrl' => get_bloginfo('wpurl').'/wp-admin/admin-ajax.php',
    'themeAjaxAction' => 'themeajax'
  ));
  echo '</script>';
}
add_action( 'wp_print_scripts', 'themename_themeajax_print_settings' );

Couple of issues: all ajax requests should be properly nonced,
it's better to use wp_localize_script() for what you're doing in themename_themeajax_print_settings()