Well, I fixed it. Must've been a configuration problem with Firefox that didn't get solved by reinstalling.

Here's what I did:
  • Closed mIRC.
  • Opened IE, told it to be the default browser, closed it.
  • Opened Firefox, told it to be the default browser, closed it.
  • Rebooted. (Don't know if that was really necessary, but just in case...)
  • Opened mIRC.

Now it works just fine, mIRC recognizes Firefox as my default browser in all situations.