Today's modern, Western biases have infiltrated our presentation of the Gospel. The Apostle Paul shows no hesitation in affirming God's desire to save families through the faith of the head of the home, the Father:
Apostle Paul: "Believe in the Lord Jesus and you will be saved, along with everyone in your household." (Acts 16:31)
Luke repeats this theme throughout the Book of Acts, too: see Ever wonder where this offer comes from? It comes from "the whole counsel of God"! (Acts 20:27) So when we read "the whole counsel of God", in other words, the entire Scripture, we ought to come up with the same conclusion.
My Attachment (see PDF below) for this post equips you with a survey covering this theme through Scripture, with a brief theological outlook. Not shockingly, the document covers all 66 books of the Bible. After you read this paper, you will have eyes to see a theme in every single book that churches have failed--no, refused!--to teach.