I had a hrose who used to do this regularly. He would get his tongue under the bit then run though the bit, tossing his head. It would end up with his mouth cut up :[ In his case it was nerves, he had been abused in the past.
A few things I tried were:
A thick rubber mullen mouth snaffle, along with a flash noseband. Prevented it, but he chewed through the rubber on the bit, lol.
A ported kimberwick. Helped, but had to have the bit very high in his mouth. Also the bit was a bit strong for him.
A rubber 'tongue layer' attachement.
It attatches to any mullen mouth snaffle and lays up the tongue. Worked, but he again chewed through the rubber so had to keep replacing it.
Bit with a tongue layer built in.
Didn't try this one, as they are super expensive, but I think it would work.
Getting the tongue over the bit is a bad habit, as it can cut the underside of the tongue and cause many problems. Itmay be that the bit is sitting too low in your horses mouth. Does he have wrinkles either side of his lips when the bit is in? If not, tighten it up.
Check his teeth, as well.
The only reason I resorted to the methods above is because my horses issue was mental, not physical. It wasn't fixable and was causing him pain, so it needed to be prevented.