Oh and by the way, hopefully he'll be fine, and when he's over this and all is well again, please do come back because you are bound to find some excellent home-cooking-for-dogs recipes here!
I think if he is throwing up (and I guess by that, you mean he's done it more than once?) -and what he brings back up looks strange -then the first thing to do is to take him to the vet as soon as you can.
At this stage I think it's more than a food issue. He needs medical attention. The best thing would be to withhold food, until you get him there, and I would go as soon as you can. Don't restrict him drinking though. If he wants to drink water, make sure it's there for him.
I can't imagine what this "stone-like substance" can be! Unless he has swallowed small stones. That would be possible if he has developed a habit of playing with them. Or they somehow got onto his food. Just a thought....does he have a "Beanie Toy" he might have ripped apart?....and could this be the filling of a toy or something he might have swallowed?
If you think so, then it's best anyway that the vet takes a look at him, as these small stones or Beanie toy filling could cause a blockage in his gut.