The problem of “you and your household”

You and your household

This phrase is used in the Bible several times.  I 'm writing about it now, because I'm working on an article about two very complex words - "believe in" - from this verse -

Ac 16:31 They replied, “Believe in the Lord Jesus, and you will be saved—you and your household.”

In order to understand this verse, we need some context, so please hang in there I provide it.  We'll be right back to you and your household (family) after that.  Paul and Silas were in prison, because of the events described below -

Paul and Silas in Prison

Ac 16:16 Once when we were going to the place of prayer, we were met by a slave girl who had a spirit by which she predicted the future. She earned a great deal of money for her owners by fortune-telling. 17 This girl followed Paul and the rest of us, shouting, “These men are servants of the Most High God, who are telling you the way to be saved.” 18 She kept this up for many days. Finally Paul became so troubled that he turned around and said to the spirit, “In the name of Jesus Christ I command you to come out of her!” At that moment the spirit left her.
Ac 16:19 When the owners of the slave girl realized that their hope of making money was gone, they seized Paul and Silas and dragged them into the marketplace to face the authorities. 20 They brought them before the magistrates and said, “These men are Jews, and are throwing our city into an uproar 21 by advocating customs unlawful for us Romans to accept or practice.”
Ac 16:22 The crowd joined in the attack against Paul and Silas, and the magistrates ordered them to be stripped and beaten. 23 After they had been severely flogged, they were thrown into prison, and the jailer was commanded to guard them carefully. 24 Upon receiving such orders, he put them in the inner cell and fastened their feet in the stocks.

That night, when everything was very dark, there was an earthquake -

Ac 16:25 About midnight Paul and Silas were praying and singing hymns to God, and the other prisoners were listening to them. 26 Suddenly there was such a violent earthquake that the foundations of the prison were shaken. At once all the prison doors flew open, and everybody’s chains came loose. 27 The jailer woke up, and when he saw the prison doors open, he drew his sword and was about to kill himself because he thought the prisoners had escaped. 28 But Paul shouted, “Don’t harm yourself! We are all here!”

It's important to understand the reason why Paul shouted out that he and all the other prisoners were still there in the prison.
Back in those days, if there was an escape from a Roman prison, the guard(s) on duty would be killed.  So here's this poor guard who's totally expecting to die a horrible death at the hands of his own people because all the cell doors opened with the earthquake.  Of course any prisoner would escape and run away given a chance like this - open doors, darkness, confusion.  Except these weren't just "any prisoners".  They were all followers of "The Way" - Christians.  And they not only stayed, they immediately began to try to convert the guard.

Ac 16:29 The jailer called for lights, rushed in and fell trembling before Paul and Silas. 30 He then brought them out and asked, “Sirs, what must I do to be saved?”
Ac 16:31 They replied, “Believe in the Lord Jesus, and you will be saved—you and your household.” 32 Then they spoke the word of the Lord to him and to all the others in his house. 33 At that hour of the night the jailer took them and washed their wounds; then immediately he and all his family were baptized. 34 The jailer brought them into his house and set a meal before them; he was filled with joy because he had come to believe in God—he and his whole family.

And there we have it - "he (the guard) and his whole family".

What is a family?

That's an interesting question - "What is a family"?  
Just as interesting is how the answer has changed over time.

We need to remember, this is Paul shouting out for the guard to not kill himself.  And, that Paul is the leader of the men in prison.  Therefore, we need to also look at the concept of "family" from Paul's reference point.  In other words, we need to look at it starting with the Jewish concept of a family.

As a starting point, in Genesis, we see this -