Implementing a non-standard protocol that only Mibbit seems to use is not a valid answer to this problem. WEBIRC is the standard solution to this, and it exist

Implementing a non-standard protocol that only Mibbit seems to use is not a valid answer to this problem. WEBIRC is the standard solution to this, and it existed long before Mibbit did. It's also about as simple and obvious as a protocol could be: the web server simply forwards the user's IP address on to the ircd at the start of a session.