I think they're confused & hiding their true identity, even from themselves, & everything that relates to that, possibly partly out of fear of losing their family. Possibly also because it's mentally very difficult for them, and you, to face.

I've known two couples to go through this & in both cases it was the wife who left. One wife fled interstate same day she discovered it, taking the kids so they never see their other parent at all (they're unable to fight it mentally). The other wife tried to stick it out as a couple but it didn't work & she's happy with someone else now.

So it doesn't necessarily mean he's hoarding to leave, or will abandon his children. It's a difficult situation & you & possibly your kids will need counselling support as well.