Using History.API to display url in ajax loaded content

custom.module.php

function custom() {
  drupal_add_js(drupal_get_path('module', 'CURRENT_MODULE') . '/CURRENT_MODULE_proto.js');
  
  $path = 'YOUR_PATH/' . $nid;
  
  if ($alias = drupal_lookup_path('alias', $path)) {
    $url = $alias;
  } else {
    $url = $path;
  }

  $commands[] = array(
    'command' => 'CUSTOM_history',
    'url' => '/' . $url
  );
}

module_proto.js

(function($) {
    Drupal.ajax.prototype.commands.CUSTOM_history = function(ajax, response, status) {
        history.pushState(null, null, response.url);
    }
}(jQuery));