I think if he is signed off with stress because of this he's probably got a bit of leeway about not bringing the grievance immediately but not much. How long's he been signed off for?
I'm going to give you my little speech which I am frequently to be seen giving people with work problems considering what action to take-
What are you not happy about in terms of your working situation?
What would a positive, realistic, achieveable outcome be for you?
What action can you take to get that result?
I think you and DH need to carefully discuss the second question. What does he want to achieve from this? I'm not going to tell you what to do. I would like you to bear in mind that if he chooses to bring a constructive dismissal claim it is difficult to prove and very stressful. He would need to bring a grievance against his boss, which would involve hearings, although not necessarily having to come face to face with his boss if that would be a problem, and I would expect him to remain signed off with stress for the duration of the process, so he wouldn't need to go into work during that time. So you need to check what his sick pay arrangements are.
The grievance may well be upheld but may be appealed against, so he might have to go through it again. Once this process is finished, if he doesn't have a satisfactory result and feels the problem hasn't been addressed and he can't possibly work there any more, he can resign and claim constructive dismissal. This would cost money in terms of lost salary while he puts in a claim and also solicitors fees.
If he wants to continue working there but wants this problem resolved, he should bring a grievance. If he doesn't want to continue working there he can either resign now and move on, or go through with the grievance, hope it's not resolved satisfactorily by the company, then resign and claim constructive dismissal. Risk is they may well take action to address his concerns which may then make a constructive dismissal claim impossible.
If they don't resolve it and he can then bring a constructive dismissal claim, and assuming he wins, you need to think about what he will have gained. Compensation may not be much, particularly if he gets another job in the meantime, and it will take months. The only other thing he would gain from winning would be a sense of justice, I don't know how important that is to him.
I would suggest you take some time over the next few days to work out what you and he want to do, come back with any questions if you need to.