Sadly, no, there isn't. And it's not mIRC's fault.
Due to caching, JOINs and PARTs are not sent immediately to a channel. They are instead batched up and sent every 10 seconds.
http://help.twitch.tv/customer/portal/articles/1302780-twitch-ircUnfortunately this doesn't even seem to be the case, where in some channels there may be users present who never appear via JOIN. Previously an IRC client could force a full list of users with the /WHO command, but they've also disabled that command.
The only possible way you can tell who is in a channel is by querying the web server.
http://tmi.twitch.tv/group/user/<user_name>/chatters