DH thinks I cheated

[EllenBach]

This is a bit complicated so might be long as I will try not to drip feed.
DH and I have been together over 30yrs and have 2 DC early 20s who don't live at home. He has a tendency to be a bit moody but on the whole we get on well and have had a happy marriage.
These last few months his moodiness has been a lot worse and a change in our circumstances mean we spend a lot more time together so it's all been pretty tense. So last night I finally pulled him up on it a and asked for explanations and it turns out that he believes (80% sure according to him) that I had an affair 5 years ago and he has bottled it up all this time.
Now this is absolutely not true and I was completely gobsmacked when he said the name of my supposed lover as I can barely remember him. It is some guy I did some admin/paperwork for and tbh I did find him a bit creepy. He was a bit over friendly but didn't make any overt propositions and I tried to make it clear that I was happily married and not interested.
Anyway I went to his place for a couple of hours a week for about 5 months (he wasn't always present and I had a key) and I was quite relieved when the job was finished. I was completely open about all this with DH and just made jokes about it all.
So of course I asked DH why he didn't say anything at the time and he said he didn't want to cause a scene and upset our DC. The reason he is so sure is that apparently he intercepted a message on our answering machine where his guy was saying he was sorry he'd missed me, so he has put 2 and 2 together and made 10.
He also then brought up an incident which happened in the very early stages of our relationship: I was still at uni, aged 20 and had a ons with another student which (future) DH found out about by reading my private diary. So because of this he thinks I'm untrustworthy and capable of cheating when I have been totally faithful ever since.
I have denied all this until I'm blue in the face but it is obviously tormenting him. He says he is ashamed of the way he feels but can't get these suspicions out of his mind.
I'm not sure what I'm really asking here except how to convince him I'm innocent and how can we move on from this.

Definite projection.

If the ons bothered him so much that he is still thinking about it 30 years later then he should never have married you.

I think the trust is gone both ways.

He cannot trust you and you cannot trust him.

He is definitely looking for a way out.

Wait... were you properly exclusively together when you had the ONS at uni? Or just casually dating but not yet exclusive or monogamous?

"Our relationship has changed recently- a house move and career change mean we are much more equal regarding income and general decision making. Maybe he feels intimidated by that."

He's lost some of his power and dominance so he's trying to establish it in another way.

"His bouts of moodiness have been more often and more prolonged. I usually just ignore him but when it's gets really bad I confront him about it. He's not outright rude or nasty just subdued and doesn't initiate any physical contact."

Withdrawing affection and the silent treatment are subtle forms of emotional abuse.

Update
DH had an appointment with his GP this morning about his persistent headaches (another symptom) and GP has told him he thinks he is depressed. He has suggested counselling and medication.
DH came home in tears but agrees now that he needs professional help.
I will support him as much as I can and hopefully we will come through this stronger although it won't be easy.
Thanks again for all your help.

That's really positive. Even getting someone to see a GP can be a major obstacle. I hope things improve for you going forward. Take good care of yourself.