I would be speaking to the company that he was subcontracting for. Was he doing it causally or did he have a contract with them?
There are quite a lot of gaps when it comes to Subby's and W/Cover. You could also contact WorkSafe in your state and discuss the accident with them, they will know whether the company is responsible for the workcver or not - but if he is casual for them it is unlikely, especially as he is new with them, there would be no evidence of what his earning capacity would be.

I am so sorry to hear about this, especially that you have questions as to how it actually happened.
When your DH is out of ICU, make sure that you mention to the nursing staff that he has been depressed lately and that he may need a psych assessment - particularly if you speak with him and you know that he did jump.

take care hun