Bekka is correct in saying that, by default, downloading your messages (to either computer) will remove them from the server, so you won't be able to re-download them on the other computer.
However, you can change that setting. To do so (in Outlook Express), go to Tools > Accounts > Mail and highlight the relevant account. Click 'Properties' and select the 'Advanced' tab. Click to place a tick alongside 'Leave a copy of messages on server'. Click 'OK' if you only want the settings to apply to the current session. Otherwise, click 'Apply', followed by 'OK'.
I've not got Vista but I assume that there will be a similar setting in Windows Mail.
Chris