I'm so sorry you're going through this. Suicide is so scary and we can't get the normal community support.
Sounds like DH's depression is so serious that it lead to an affair. Without the affair, he's even more destabilized. Is suicide something that has happened before in his family? This can be really hard to find out. But that's usually the "why".
Whether or not to hospitalize is a really tough call and best left to a clinician, medical or mental health professional. Please don't put that burden on yourself. One of the psychiatrists I work with told me about IPAC, part of Inova Fairfax. It's an urgent care for adult psychiatry. Same-day psychiatric assessment and medication management, which is what folks mostly get when they're hospitalized. Regular business hours, not 24-7. For others possibly reading this, not for teens. Lots of highly trained psychiatry interns and residents:
https://www.inova.org/locations/inova-psychiatric-assessment-center-ipac
Medication a must (it does wonders).
At least 2x a week individual therapy. Medication provider will likely have people to refer to and there's always Psychology Today.
For work, I'd maybe recommend talking to a lawyer. The Women's Center, I believe, has lawyers who will give free consultations.
I have not read every word of the comments as I'm in the car now, but if you are not, I really hope you give yourself some time in therapy to process this and learn how to support DH and the kids. It's a lot and at a certain point friends can only do so much. You've got this.