I think your solution may lie in using the "Identities" feature in Outlook Express so that individual identities can be set up for each member of the family with only their own POP3 mailbox set up within the identity.
This does, of course, mean that each must have their own email address, not simply an "alias" of a single email address. Many ISPs offer unlimited email addresses but in reality they are unlimited aliases for a "single" email account. You need to have separate email accounts.
If you use Outlook, as opposed to Outlook Express, I'm sure there is a way to do something similar but, knowing Outlook, it will be considerably more complex!