It is certainly YOUR decision on how to handle this, but IMHO, I wouldn't count on H telling his parents the entire truth. He will only tell them what HE wants them to know, and he is more likely to do this with you not being there to see it through.
I would ask him what time he plans to be at his parents' house, then say, "Good, I'll see you there." Then BE THERE. If he chickens out, then proceed to tell them yourself.
Get it out in the open and over with. No more excuses on both sides.
(((((((You can do this.)))))))
Getting over a painful experience is much like crossing monkey bars. You have to let go at some point in order to move forward. ~ Joseph Campbell