How is the deductible applied in an overlapping coverage situation?

I am in a situation where I was laid off shortly after my daughter was born, so she has a period overlapping coverage under mine and my husband’s insurance plans.

We are both on Anthem. My plan is better than his, 10$ copay, 0$ deductible, EPO. His is an extremely high deductible plan that requires an HSA. His is the primary simply because his birthday is before mine. I requested mine be primary, but they refused (and apparently it’d be considered insurance fraud if they tried to do that).

My question is, when I file the claim for her hospital care after birth with my husband’s plan as primary, will we have to pay the very high deductible? Or will that get covered by the secondary (EPO 0$ deductible) plan?

I have been in contact with Anthem all day trying to get an answer to this question, and have been given the run around. One agent said they can’t tell me until I file the claim. Another agent said I’m still looking into it over and over until she finally just ghosted me.

Has anyone else been in the situation before and have any insight? I seriously have a hard time coming to terms with the fact that I may end up paying thousands of dollars instead of 0, simply because my husband’s birthday is before mine.