Wa-`alaykum as-salam wa Rarahmatullah wa Barakatuh
In the Name of Allah, the All-Merciful, the Mercy-giving
All praise is due to Allah. Peace and blessings be upon His Prophet Muhammad.
It is not clear from the question whether you were Muslim or non-Muslim when you got married to him. So, we need to deal with both cases:
If you were Muslim, your marriage contract was primarily invalid from the Shari`ah point of view which means that you have never been a husband and wife at all.
If you were non-Muslim when you got married to him, then, from the time you have converted to Islam, he has become unlawful for you as a husband. Allah Almighty says what means, “O you who believe! When believing women come to you as emigrants, test their [sincerity]- and it is Allah [alone] who knows best about their faith. Thus if you find them to be believing women, then do not return them to the disbelievers. They are not lawful [wives] for them. Nor are [the disbelievers] lawful [husbands] for them.“ (Al-Mumtahanah 60:10)
Based on this clear injunction, Muslim scholars unanimously maintain that a Muslim woman must be separated from her non-Muslim husband. If the husband accepts Islam during her waiting period, they may continue their marital life; but if he refuses to accept Islam, she may marry a Muslim man after the end of her waiting period.
In both cases, it is obvious that there is no need for divorce on the part of the non-Muslim man from the Shari`ah point of view but I wonder if laws in your country require this. If so, you may consult a lawyer or refer to the nearest Islamic centre to settle the issue.
Allah Almighty knows best.
Views expressed by hosts/guests on this program (live dialogue, Facebook sessions, etc.) are their own and their appearance on the program does not imply an endorsement of them or any entity they represent.