electrical prob (headlights kill my car)

Ok i have a problem my 94 5.0 car runs great except when i have my head lights on it takes 10-15 min. and the ignition suffers a power lost and car barely runs this only happens with headlights on and before the car suffers the power lost it has a bad miss just with headlights on
 
also it has a new alternator new distributor, cap, rotor, coil, and plugs, tested batt with volt meter its got a little over 12v with car off, and with car running its got 13.44v with lights on and 13.99 with them off. Any ideas will be greatly appreciated.
 
i think your alt. is dieing. it should be putting out over 14 vdc running. pull the alt and battery and have it tested. the battery should run the lights for more than 10-15 minutes too. ck your batt cables too, you might have corrosion inside the insulation
 
update didn't mention with my a/c on that it makes it worse i changed the cable from alt. to distribution box and cleaned all connections now with headlights on and a/c off i get 14volt at alt. 14volt at battery and picked up 1v0lt at coil its a little over 13volts car runs much better now. but put on a/c and it pulles it down.
 
Thanks for everybodys input. I didn't even think about the circuit protection but i will when i get in from offshore, got till next tuesday to figure out whats wrong. and also when i changed out charge wire i checked all other cabels. thanks agin