First he walked with God...

"But Noah found favor in the eyes of the LORD...Noah walked with God." Genesis 6:8-9 The precursor to Noah having children: Noah walking with God. Noah had already established a relationship with God, he had an intimacy such that God would find him to be called "righteous" and "blameless," not because of his great deeds, but because of walking with his Savior. Then, God called him to have children: Shem, Ham and Japheth (Genesis 6:10). Subsequently, God calls Noah to build an ark and take his whole family aboard for the upcoming flood... Wait... the upcoming flood?? There had been nothing of the sort before! In Genesis 7-8, we watch Noah's family, without any scriptural mention of complaint or question, get right on and off the ark. That means, that Noah's whole family had a trust in Noah as well. His family followed his lead.

It is likely that Noah did not keep his faith to himself, but that his family knew of it and had reason to trust it and his hearing of the Lord's voice. It is also possible that they also heard confirmation from the Lord, but scripture doesn't tell us that specifically. What scripture does choose to reveal to us is that God told Noah and then they all got on the ark; and that God told Noah and they all got off the ark.

I believe that Noah likely had a relationship with his family that entailed Biblical leadership as mentioned in Ephesians.

Ephesians 5:23-27 "For the husband is head of the wife, as also Christ is head of the church; and He is the Savior of the body. Therefore, just as the church is subject to Christ, so let the wives be to their own husbands in everything. Husbands, love your wives, just as Christ also loved the church and gave Himself for her, that He might sanctify and cleanse her with the washing of water by the word, that He might present her to Himself a glorious church, not having spot or wrinkle or any such thing, but that she should be holy and without blemish."

God desires us to be humbly submitted to Him (even though we don't always have all of the information!). Noah had only but the Lord's voice to let him know that the flood was coming as his wife only knew that the flood was coming by Noah's voice (and perhaps the Lord's). The children only knew of the flood coming by the parents (and perhaps the Lord's). God has set up this system to build our faith. He desires for us to be washed with His word and presented back to Him as holy (set apart) and without blemish! So, God sets up these ways that He can build our faith (sometimes they are trials) so that we can be perfect and complete and lacking nothing (James 1).

This system is set up within the family not only to build trust in each other and interconnectedness but the same with the Lord, but the same is for the body of Christ. For instance a fellowship of believers at church or Bible study: these people are available to have the older teach the younger and to foster a more intimate relationship with Jesus Christ for both parties.

I believe that parents are called to live their lives as a living sacrifice, just like God did, giving Himself for us, dying upon a cross for us, raising from the dead to show us that He has power over death and life. Parents are to live their lives in front of their children, pointing to the one who gave them life.