I think I found 2 useful links:
The first is a Firefox and Thunderbird extension that can protect your profile with a password.I haven't tested it for portability and I think the protection isn't very strong but it may suffice for average stuff.
The second is a Thunderbird extension that lets you brows within Thunderbird. I haven't tested this one either so I don't know what browser it uses.
Just wanted to share them with the community. 
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There are a lot of great functions that you can get with the Mozilla Extensions.
I just found one called Launchy, that can be installed to FF and/or TB.
It lets you choose the program to use when opening a link, so (for example) if you want to open a mail link with your personal Portable Thunderbird instead of the locally configured default mail editor, you can.
I'm not sure where it gets the list of programs you can use; however, you can create an XML file to point to specific programs, and you can use relative links, so you can make sure you are choosing your portable app on your stick.
I made this half-pony, half-monkey monster to please you.
I had tried ThunderBrowse for a bit a while back, it's not bad.
Two addons that I know are portable and work very good:
SafeCache -> https://addons.mozilla.org/en-US/firefox/addon/1474
SafeHistory -> https://addons.mozilla.org/en-US/firefox/addon/1502
Both are security/privacy protection addons.