Firebug works both with HTTP and HTTPS, but what it doesn't do is show you the SSL/TLS details under the HTTPS connection.
Are these handshaking, keyexchange, cypher exchange messages carried through HTTP protocol requests/responses or are they separately done through some modules built in the browser as a SSL/TLS module and therefore cannot be viewed through tools like firebug?
The SSL/TLS handshake is not carried over the HTTP protocol, but it's done at the SSL/TLS level, under HTTP (HTTPS is HTTP over SSL/TLS). This is done in Firefox by the NSS library (part of Firefox and the Mozilla project).
You might be able to see more details by using a tool like Wireshark.