I would advise you to:-
Make notes so that it is all set out clearly for when you contact the union rep. Do this in chronological order. Include a photocopy of the letter your dh has received and anything else that would be useful for the rep to keep. If there is a choice of reps, ask who has the most experience of dealing with a)this problem and, maybe, b) the people in work concerned.
Go on the Citizens Advice Bureau website. Find out where your nearest office is and make an appointment for you or your dh to go and see them. On the website you will find a whole chapter on disciplinary stuff. You need to inform yourselves of your rights and the procedures you should follow. Don't assume that the people in work will tell you clearly what you must do and by when, or necessarily follow the correct procedures themselves. They're only human and some go about these things very badly and treat people poorly. They also make mistakes in procedure that can make the whole disciplinary procedure invalid. N.B. You, also, need to follow the procedures to the letter.
If there is a staff handbook in your dh's work on what is expected of you re:- contacting them when you are sick, then read up on it. Show how you have done your very best to comply with the rules and put a consise explanation in your notes of the occasions when you weren't able to comply.
You can ask your dh's gp to write a note in support. I did and it was most effective. It cost £10. If you were to do this, you should discuss it with the gp first, giving him a copy of the letter from work, so that he can word it to address their concerns.
As fisil said, occupational health can help. I would say that your dh should say that, yes, he is willing to go to the occupational health doctor. The o.h. dr will send a report back to work advising them of what adjustments they may need to make to your dh's hours, work or to the sickness absence procedures, perhaps. He will probably be on a review, say every 3 to 6 mths or something. I would say that maybe your dh should have you or someone else he trusts to go with him and maybe go into the room with him also. Your gp sees you often enough to read between the lines. Someone you haven't met before can't do this and needs you to either express yourself clearly (very hard when you are depressed) or have someone sitting with you who can hear the question being asked and answer it consisely and accurately.
Sorry if this all sounds "Do this. Do that." I hope it helps and good luck!
P.S. I should have put mention of the employer's "duty of care" in there, somewhere. Try to find out what that means in your case. Also, definitely your dh should have representation in any meeting. You need to make notes in the meeting, probably the union rep would do this. It might be a horrible thing to go through and he needs all the support he can get. Think of a good time and date and location to make it as easy as possible for your dh. Don't agree to the date, time and location without saying that you need to check that the union rep can make it.
Good luck again.