I haven't seen this show, but I would say I have a traditional marriage, my husband works full time, I keep the home and care for the Children, garden, pets and elderly freinds, athough we are both involved with the children and their education.
We are also fairly traditional, (while also being unconventional) in our practice of Christianity. Aiming for pro-life, non-violent, non political, simple living, modest and practical :new testament style Christianity.
In addition I try to dress in a feminine but modest style, cover my hair for worship. This is my husband's request but he wouldn't insist if it were not my conviction.
My husband in principle has the final decision if we disagree, as I did promise to "obey" in the marriage vows, 20 years ago. ( Athough at the time I don't think I gave it much thought, I do however consider it, as the other vows a sacred promise before God). In reality though my husband is a gentleman, considerate of the needs of his family and has rarely made any big decisions without my input and as time has gone on we are more of a team, all be it with different but complementary roles.
I find it a very satisfying, simple, enriching and peaceful way to do family life. But I do think, what is described here is a little extreme, especially the discipline ridgid adherence to rules and roles.