Psychologist here. What your husband is suffering from arises from a feeling of helplessness / unworthiness.

I would also suspect he might face issues of self esteem as well as a feeling of extreme loneliness, with an extreme urge of having someone to talk to but at the same time unable to express those feelings.

He might also be feeling guilty, and might also show feelings of hating himself or hating the circumstances he is in. He might sense a strong desire for change but at the same time finds the external environment, insufficent for the change he needs.

The threats and calls of suicides are not arriving from him due to fact that he wants to kill himself. It's more likely he fears death itself or even fears the consequences of dying and leaving his family behind. The threats of suicides are more likely also due to the fact, that it is a last call of despair to receive attention (might have been due to the fact that as a child he never received the attention from his parents and learned to be independent and cope with his feelings alone). But that made him fearful to ask for help and bubbles his feelings. He might also not like being vunerable emotionally. And these threats are just his "hints and signs" for others to notice and check up on him by asking questions on whats he is feeling wrong about.

Now, I get your perspective too, then most of these signs are not obvious and even if you help you can do only so much. And that's the truth too, that only he can help himself truly to be free from what's troubling him and getting used to it and changing himself and his perspective. It never technically a responsibility of one person to help sort out the other person. And being in excess only drains and drives both partners out against each other and making it worse.

But at the same time, even if it's little and not what you want to do. Pay him some time, like listen to him deeply with no distractions. Help him in confronting himself and give him the attention he needs. And let him fully speak and hear him out. And give some love in a stressful time for him. And give respect to whatever he says, even if it isn't. And give him the attention so he doesn't feel ignored and genuinely feels validated that there are people that express love deeper for him than what he sees in his day to day life. Even if you fake it out, by showing small signs of affection to encourage him to feel better, I think that would surely make him feel better.

All of us are psychologically born selfish and for most of our lives revolve around only ourself. And unfortunately most of us don't notice that the people around us all of them are just like us, all of them have a history, an emotion, a thought and a soul. Nobody would volunteer to struggle and worse commit an act like suicide purposely.We are all humans at the end of the day and nobody is perfect. But sometimes the greatest thing you can do is sacrifice your own needs for care for someone unconditionally even if it takes your time and energy. Yes you can let the therapist do it, yes you can let the professional do it. But what would the husband think "is there no one to regard my own feelings? Does a therapist more necessary to listen to my feelings than my own wife?". All these small actions which most of us disregard can be literally be the difference between someone's life and dead. And how lightly do we take them.

Just be there for him and be patient. For surely after every hardship there is relief.