USA airport > Mexico City > Zihua Customs twice?

I usually fly direct from Chicago to Zihua. That flight wasn’t available this year. Instead, I have a layover in Mexico City where I’ll catch my flight to Zihua later that day. Can someone tell me if I have to collect (then recheck) my luggage in Mexico City, where I assume I’ll be going through customs? (I actually don’t mind and besides have 4+ hours between flights.) Another question: do I have to go through customs again when I land in Zihua? Since I’ve always flown directly from the US to Zihua, everyone on my flights goes through customs. I’ve never seen what happens when planes arrive from another Mexican airport. Many thanks!