OK - for any of you who WANT this behavior, like me .....
There are two places you need to configure this.
The first is the "Track URLs" option that you can set by right-clicking on the channel tab.
The second is in the main mIRC options menu. (Click the options icon, go to Tools->Options, or click Alt-O.) In there, go to the IRC group, and click on "Catcher." Under "Enable catching for:" at the top, check the "URLs" box. This screen is also where you can make some other adjustments to how your system will behave when launching URLs.