I've had HA for years. When it takes its grip its very debilitating and I feel it's not something I can ev7get over.
However, I dont parade it about like your DH. There does seem to be a narcissistic element to his anxiety. When mine flares upto its worst , i tell DH my symptoms I case I die suddenly and he has to tell the hospital my symptoms, I take myself of to the spare room and read, watch tv, jigsaws etc out the way, whatever takes my mind off my issues. Doesn't always work but I have stopped googling.
My DH is pretty good. Yes, he's probably fed up, but he firmly tells me not to give it head space, to stop talking about it. And he is firm. I mean, I cant have lung cancer, a brain tumour, dementia, a blood clot, heart disease and the start of MS all at the same time, and he makes me see I'm being irrational.
My advise is to be firm, and stop the conversation dead dont allow him to wallow in his ailments. It's not good for him and certainly not for you. Walk away to another room but dony engage in long talks, allowing him to rant on and on. However I suspect he actually enjoys thinking he has a serious illness. He's enjoying the whole dynamic of everything being about him. That's a whole different issue.