It isn't usual for this behaviour, even when developing MVC websites. I am able to make changes to non-compiled stuff (aspx,ascx) etc and it'll take effect immediately on refresh. Changing classes will require you to stop debugging so that you can re-compile, and allow breakpoints to work correctly.
Also, whilst isn't strictly an answer to your question, you should strongly consider moving away from the baked-in Cassini web server used when debugging.
For more information on my general hatred of Cassini, please read this previous question.
If you're unable to either install IIS on your machine (because it might be XP Home or whatever), then you should consider either upgrading to XP Professional (where you are limited to running one website only), or Windows Vista, or Windows 7 RC where you can use IIS7 and all the greatness that it provides.
If you can't do any of those, you should consider trying an alternative, such as Ultidev.