Yes, companions normally are restored to full health after a fight.
But if they get crippled outside of a fight (for example a land mine) they remain crippled until the next fight is over then they heal.
They can also use Stimpacks but that's only in a fight, I think.
So picking a fight with a molerat or radroach is a good course of action.
...l (BTW Jericho kicks ass)
He sure does! He's my favorite companion. Mostly because of his comments.