Brucie, you're not alone in that question, but midnight being 12:00 a.m. is just one style — and in many cases not very informative. The logical extension of that reasoning would be to call noon 12:00 p.m., but you can't call it "post-meridian" when it's "meridian."
I used to run into the "midnight" problem all the time when I was a newspaper editor because reporters would write that a strike was set for "midnight Monday" and leave us to figure out what that meant when we were editing it at 3 a.m. Friday morning.
I argued that midnight means midnight, but it can't specify a day. I convinced the powers that be to make it a style point for reporters to write that the strike begins at 12:01 a.m. Monday or 12:01 a.m. Tuesday. Solved the whole problem.
I also got them to ban the use of "biweekly" and similar terms because they can mean either twice a week or once every two weeks.
Ain't time language weird?