When Paul and Silas were in jail and the earthquake came and opened the doors and loosed all the prisoners bands, the jailer came before them trembling and asked what he needed to do to be saved.  They told him, 

"...Believe on the Lord Jesus Christ, and you will be saved, you and your household."  Acts 16:31 NKJ

When you believe in Jesus Christ you are saved and you have a promise for your 'household' or your family also.  We read promises for our children also such as:

"There is hope in your future, says the Lord, That your children shall come back to their own border."  Jeremiah 31:17 NKJ

"All your children shall be taught by the Lord, And great shall be the peace of your children."  Isaiah 54:13 NKJ

"...The seed of the righteous shall be delivered."  Proverbs 11:21

The Lord cares about the salvation of your loved ones!  

Your loved ones may believe in the Lord but may not have the fervor you would like them to.  You might be wondering how sincere their decision is.  The best thing to do is to pray for them.  If you talk to them about what you perceive to be a lack of spiritual interest you may do more harm than good.  The Bible tells us that when we are born again we are a babe in Christ.  The thing that will get a person to grow spiritually is the Word of God. 

"As newborn babes, desire the sincere milk of the word, that ye may grow thereby:"  1 Peter 2:2

The Word of God will cause a person to grow spiritually.  But when a baby is born you don't take the whole bottle of milk and cram it down their throat!  You don't try to feed them solid food too soon either.  But a steady and consistent diet of the milk of the Word will bring growth.  If it seems your loved one is lacking that desire for the Word then pray about it.  Ask the Lord to show you what you can do (if anything) to encourage them along but be careful not to cram the Word down their throat or argue with them about it   They need the Word to grow and a spoonful of the pure Word of God goes a long way!  They need to hunger for the Word and many times when a person sees the joy, peace and victory that the God brings to your life then they will begin to desire the same thing.  

When a person is born again the seed of God's Word has been planted in their heart, (1 Peter 1:23).  It is an incorruptible seed!  And you can be confident that the Lord does not give up on a person.  

"Being confident of this very thing, that he which hath begun a good work in you will perform it until the day of Jesus Christ."  Philippians 1:6 

You can be confident that just as God is continuing to perfect the good work He's started in you He will do so in the lives of your loved ones also!

God Bless you and have a great day!