If you remove family from the formula then the continuity dies.
It really can be a treasure if the whole family could see it the same way, but i really think that Jesus would rather we not even talk about the Gospel if we have to water it down in order to get some one else to except it.
Some people will insist that we add to the scriptures in order to please them and others will insist that we leave things out, we should do neither one and neither should we try to explain those things we do not understand.
Mat 10:34 to 39
Do not think that I came to bring peace on Earth; I did not come to bring peace, but a sword. For I came to set a man against his father, and a daughter against her mother, and a daughter-in-law against her mother-in-law; and a man’s enemies will be the members of his household. He who loves father or mother more than Me is not worthy of Me; and he who loves son or daughter more than Me is not worthy of Me. And he who does not take his cross and follow Me is not worthy of Me. He who has found his life will lose it, and he who has lost his life for My sake will find it.
It appears that Jesus is saying that this is what will happen in general when some one in the family turns to Christ but i don,t think he was saying that the whole family could not be saved, although i believe it would be a rare thing.