Maybe I read through this thread too quickly, but since you all seem to have tried a few combinations, I figured I'd mention one I didn't see already mentioned.

Code:
/run "a" bc


The line above works for me. If you had an "a.bat" batch file as shown below...

Code:
"c:\program files\internet explorer\iexplore.exe" %1


...then ran the following line in mIRC...

Code:
/run "a" google.com


... google should pop up in Internet Explorer fine. Sorry if I'm repeating what someone else already said.