All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If your husband has truly believed in Allah and His Prophet before he actually married you, then his previous belief or creed, has no influence/impact on your marriage, neither has his lineage.
However, he should now perform Ghusl for embracing Islam, as most scholars believe that when the Kafir becomes a Muslim, he should perform Ghusl. Abu Daawood reported from Qays ibn ‘Assim that he said: "I came to the Prophet to become Muslim and he ordered me to perform Ghusl with water and Sidr."
Moreover, know that the road to guidance is easy and paved for any one whose aim is to fulfill its conditions and avoid its nullifiers. To achieve this, you should stick to the following:
1) Being true and sincere in seeking guidance, since anyone who is sincere with Allah, Allah will not deceive him. Allah Says (what means): {"If Allah knows [any] good in your hearts, He will give you [something] better than what was taken from you, and He will forgive you; and Allah is Forgiving and Merciful."} [Quran 8: 70]
2) Learning useful knowledge since actions cannot be right unless done with knowledge. This is the reason Allah has put knowledge before speech and work. Allah Says (what means): {So know, [O Muhammad], that there is no deity except Allah and ask forgiveness for your sin and for the believing men and believing women.} [Quran 47: 19]
3) Being keen to increase Iman by multiplying good deeds, fulfilling obligations, and staying away from sins and vices.
4) Having firm belief that the adherence to the Orders of Allah is the only source of happiness and comfort in this life and the Hereafter and the opposite is the source of bad fate in this life and in the Hereafter.
5) Befriending only righteous people and staying away from evil ones.
But if a man marries while he is still Kafir (non-Muslim), then the contract is invalid and must be cancelled as Allah Says (what means): {… then if you ascertain that they are true believers, send them not back to the disbelievers, they are not lawful (wives) for the disbelievers nor are the disbelievers lawful (husbands) for them.} [Quran 60: 10]
Now, after Istibra'a (observing one menstruation period – to make sure she is not pregnant) the former wife and husband may make a new marriage contract if they like.
Allah knows best.