Hmm. Him being a freeloading cocklodger is one explanation, but there are others.
I feel your pain, OP, and have a similar situation. Although in mine, the DC are school age. It might have gone on longer too, although the pattern is very similar: DH is a freelance designer and I've been the higher earner for 5 years, the main earner for 5 years and the sole earner for 5 years (ish). I've done the conversations, the support, the taking equity out of the house to plug gaps, and the ultimatums. It's not effective, because in my case its not that he's workshy, it's that his confidence is on the floor and he fears he won't succeed and becomes very risk averse, aims lower and lower, and has completely lost sight of what it means to be half of a partnership. Each conversation fills him with shame (not that I shame him. He's ashamed of his failure to provide). Each ultimatum paralyses him with fear that I'm going to end things and he just blanks it and moves past, carrying on and hoping I will drop it. So far, I have, because I'm earning enough for us to live on, and because the DC are young, and because companionship is better than loneliness, and, yes, because a split would be expensive and I'd be the loser.
So, I sympathise. But understanding that it might be more complicated than pure laziness doesn't mean I know what the solution is.