Does anyone know if children are eligible for CHIP if they are also eligible for health insurance through a parent's employer?

I'm currently pregnant with twins (first children) and we are considering whether DH should be a SAHD to save money on childcare costs. His wages would not cover childcare for two.

My employer charges ~$400/child or $715/family (which I'm assuming is a spouse and two children) for a high deductible HSA plan. The cost for the no-deductible EPO plan is $790/child or $1250/family. I think the EPO makes more sense for babies as they'll be at the doctor a lot (and for me during my pregnancy, though I can't switch until September). However, $1250 is half of what I take home in a month. Our mortgage is $800 so we obviously cannot survive on ~$1300/month. And other entitlement programs like WIC and food stamps look at gross income, not net, so I make too much to qualify for those, even for a family of four.

With my income alone they would be eligible for CHIP according to the income guidelines. But I'm hoping that the possibility of getting insurance through my employer does not disqualify them.

Any insight is helpful, thank you!