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.