If you right-click the account in the (left) Folder Pane, Subscribe, click Refresh, does the Archive folder appear in the list with a check mark?

The Archive folder is not displayed in the folder tree of the Subscribe dialog. Clicking the Refresh button does not affect this.

It appears you can do this by setting up a second account in TB with the 'IMAP server directory' set to "/archive/".

I'm tried this. Sorry, it's not work for me: 1. When I create second account in TB I've got the error message that account with same credentials already exists. 2. In order to prevent error I entered username as DOMAIN\username. It's works for me. 3. Then I wrote "/archive/" in 'IMAP server directory' field and saved settings. INBOX folder started sinchronization. 4. I've choose menu item 'Subscibe' and in dialog window i've got the empty folders list. Refresh button don't take affect on this.

You can't have two accounts with the same Account Name, but I'd recommend you not use the \ or / characters in an account or folder name. Name it something like usernameARCH. Use the correct User name for the 2nd account, which is usually the email address, and try /archive/ (no quotation marks) for the IMAP server directory. Unfortunately, I don't have an Exchange account to test this.