In the US, he would owe child support based on the difference between his income and yours - and yes, if 50:50 custody was arranged, then he would not owe child support.
Not necessarily true. In many states, including mine, even in 50/50 arrangements the "more monied spouse" pays child support. That's how my ExW had an affair, divorced me, and still gets monthly checks from me even though I watch the kids at least as much and usually more than her. What a system. In your case though it's your H who's the bad actor and makes more so depending on where you live you'd get child support even if you eventually go 50/50...consult a L on this!!!
Me:39 Ex-W:37 M:7 T: 9 S:6 D:3 BD/IHS/Confirm EA/PA: Feb '20 OM1 affair ends: May '20 W/OM2 & moves out: June-July '20 W files for D: Jul20 OM2 confirmed: 9/2020 Divorced: May '21