If there is one thing Microsoft and Google should be able to get along with is not working well with IMAP. For some reason, they don't support the IMAP protocol well, even though in my humble opinion it is the superior protocol.
I just emailed this to a client:
I think what you want is to use the IMAP protocol instead of the POP3 protocol. That will allow you to have everything on your desktop and the website be the same (including sent items), but it is a challenge to get the items from your desktop onto the server. Also, Microsoft Outlook doesn't work well with IMAP.
The way it is setup now, the incoming items should stay on the server. Its not exactly what you are looking for, but its as close as we can go without having to really change the way your computer is setup.