What did they bring to the fight that was unique to the militia?

Probably some muskets and bayonets.

The vast, and I mean vast, majority of the Continental Soldiers stood in line and traded volleys with the British. The British also had local loyalists who fought the same way our irregulars did.

I believe General Nathanael Greene had the best strategy for incorporating the militia. He put the militia well forward of the line of Continental Soldiers. They had a huge advantage in the effective range of the long rifles over the British muskets. He instructed them to take a few shots to include shooting British officers, then retreat past the line of soldiers and continue firing from the forest. In one battle, the British saw the militia retreating and believed they had the advantage and broke ranks to chase the militia but ran into the line of Continental Soldiers. We won that battle, but I don't remember which one that was.