In the beaten-up MVC pattern, the Servlet is "C" - controller.
Its main job is to do initial request evaluation and then dispatch the processing based on the initial evaluation to the specific worker. One of the worker's responsibilities may be to setup some presentation layer beans and forward the request to the JSP page to render HTML. So, for this reason alone, you need to pass the request object to the service layer.
I would not, though, start writing raw Servlet
classes. The work they do is very predictable and boilerplate, something that framework does very well. Fortunately, there are many available, time-tested candidates ( in the alphabetical order ): Apache Wicket, Java Server Faces, Spring to name a few.