Sigh.

Turn your headlights on. Measure across the battery. if >12v, battery is ok.
Then, get an FSM, and start tracing the path from the battery to the headlights. Once you drop below 12v, you've found the problem area.

The "car" dropping power, and the battery dropping voltage, are very different indicators.

If you've checked your battery, relays, fuses, and grounds, then your electrical system has to be working, since thats all there to it. Obviously, you've missed something.