Chrisler extended the invitation after Perkins' May 24 appearance on CNN, where he said he wasn't going to be silent while gay people tried to redefine marriage in the US, change what his children are taught in school and what religious organizations can do.
Asked by CNN's Brooke Baldwin if he'd ever been to the home of a gay couple, Perkins said he had not.
Chrisler's response: "I would like to extend an open invitation for you and your family to visit my home and have dinner with my spouse and children with the full hope that you will witness the love that exists in our families."
Perkins' May 28 response, read out on CNN: "My wife and I will be glad to respond when we receive the invitation to find a time that works."
Chrisler told CNN that she didn't necessarily expect him to accept but says that if the dinner does come to pass, it'd be great for Perkins to get "a glimpse" into the lives of the one million gay and lesbian parents who raise two million children in the US.
"It's not one family here or there; it's a significant number of kids we're talking about," Chrisler points out.
"What bothers me is when people who haven't taken the time to know me, and to know my children and to know my values, talk about me and then espouse hateful rhetoric that my kids hear, that the children like them hear."
Watch excerpts of CNN's interviews with Perkins and Chrisler here.