You set them up so you have to File | Switch Identity to go from one to the
other? If so, go to Tools | Accounts | Mail in each identity and make sure
the other is not listed.

If your email addresses are all "aliases" for one mailbox, you'll still need
Message Rules when using separate Identities.

Most families (an intentionally all-encompassing term) will have one Mail
Account with their one ISP subscription ($$/month for all).  Most ISPs
provide you with multiple Addresses for the Mail Account (e.g., Me@ISP.com,
You@ISP.com, etc.) but all of them "point" to the one mailbox.  As such,
each Identity will need to use Message Rules so that only mail addressed to
them is downloaded into their Inbox.

The following refers to two addresses, but you should be able to follow it
and amend for three or more.

Me@ISP.com and You@ISP.com are aliases for one Mail Account (mailbox).  In
the Identity associated with Me@ISP.com, create a Message Rule stating,
"Where To or CC contains You@ISP.com, Do not download it from the server"
and place this rule at the very top of the list.

Then create a similar rule for the Identity associated with You@ISP.com
directing any messages addressed to Me@ISP.com not to be downloaded from the
server.

Also see MVP Tom Koch's fine pages on using Rules:

Message Rules Tips
http://www.insideoe.com/tips/rules.htm

Why doesn't my rule work?
http://www.insideoe.com/faqs/why.htm#rules

Does each identity have only 1 e-mail account defined within it?

Are the 2 e-mail accounts actually separate accounts or just aliases
to the same mailbox?  If they are aliases, you can never separate the
one mailbox from all aliases assigned to it.  At best, you can use a
rule that looks at the To/Cc headers to differentiate your e-mails.
You could also use a rule to check through which account (defined in
OE) the e-mail was received to move them to different inbox folders.