function doGet() {
  var app = UiApp.createApplication();
  var t = app.createTextBox().setName("tbox").setId("tbox").setValue("set before invoking handler");
  app.add(t);

  var h = app.createServerHandler("myHandler").addCallbackElement(t);
  var chk1 = app.createCheckBox().addValueChangeHandler(h).setValue(true,true);

  Utilities.sleep(500);
  t.setValue("set after invoking handler");

  SpreadsheetApp.getActive().show(app);
}

function myHandler(e) {
  var app = UiApp.getActiveApplication();
  SpreadsheetApp.getActive().toast(e.parameter.tbox)
  app.getElementById("tbox").setValue("set in handler!");
  return app;
}