(Update: for clarity) Starting with the login Http get/post use https and use https through out the user's logged in session.
Use Http only when there is no logged in user.
There is a reason that cookies are not allow to cross protocol boundaries - it is an attack vector! (* see update below)
How to do this very bad idea
If you really insist, encode the jsessionId in the redirect to the http url ( or always encode the jsession id in the url). When Tomcat gets the http redirect, tomcat should find the session and continue.
Why you shouldn't do this
Seriously, any site that mixes https and http content on the same page is just opening themselves to all sorts of fun (and easy) attacks.
Going from https to keep the login "secure" is pointless if the rest of the session is in cleartext. So what that the username/password (probably just the password) is protected?
Using the ever-popular man-in-the-middle attack, the attacker just copies the session id and uses that to have fun. Since most sites don't expire sessions that stay active, the MIM effectively has full access as if they had the password.
If you think https is expensive in terms of performance look here, or just search. Easiest way to improve https performance to acceptable is to make sure the server is setting keep-alive on the connection.
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