I believe he believes it all 100% but I believe he also knows if he was to tell the wrong person they'd have him thrown in the asylum quicker than he could say 'I'm joking' *
"Thrown in an asylum " is not his future.
Admission to MH in-patient wards is the last resort of mental health treatment not the first; and it won't happen unless either, he agrees to it voluntarily , OR, there is evidence of him being a danger to himself or others.
There are effective medicinal treatments that can help relieve the distress, anxiety and fear these delusions are causing to him. He can get better. You need to believe that as much as he does. Not least, so you can reassure your children. Daddy is ill, but doctors can help him.
From what you say, it sounds as if he is actually aware of being mentally ill (and so scared of the implications, he's trying to hide it and deny it). There is a positive to that. MH patients who are aware of being ill, have a head start on MH patients who have no awareness at all.
Last century, cancer was so misunderstood, hard to treat, terrifying, that people denied having it; often families denied the patient had cancer; and that degree of fear, shame, stigma and ignorance prevented people who could have been treated, from getting the help they needed. Now, people know more, treatment has far advanced, and plenty of people with cancer live a normal everyday life.
Some mental illnesses are still in the same dark age of hide/deny cancer used to be.. People are ashamed, keep it secret, won't admit, so don't get the help they need. We've just about reached a point where people admit to anxiety, or depression and know there is treatment that is effective for many. But they still don't know about or understand paranoia and delusions (two of the commonest symptoms of more severe MH) or that they are treatable.
Get yourself the support and help you need, to understand what is wrong with him and that there is treatment and hope for him.
You never know; if he sees you acknowledge the mess he's in and get some support for yourself, that might persuade him he really needs to do the same.