To Julie,
I'm from muslim moderate country in Malaysia, i know your how you feel in this situations,i have my own opinions as what Islam that ive learned - If were convert to islam and the husband are not- it is automaticly the divorce.because he is not your mahram now,stay with a man which is not mahram with you is haram.I know he is your husband BUT u need to think positively that youre a Muslim now and your husband not.he is your husband when youre still not muslim,Islam is your new religion now,so If your husband want to convert to Islam, you and him must marry under Islam law.
Im not try to being mean but this is what we had learned about Islam and Hukum Hakam.
Thats why Islam being practice to be together about having Islam in a relationships.What were you doing now is Zina,bcoz he is not your husband anymore,he is only the father of your kids.
Maybe your Mazhab is isnt same of what we had in here.We also having the same case of what you heading now.
Guy convert to Islam and his wife is not,it is automaticly divorce,so theyre live separate place until his wife decided to convert and married under Islam law.Unless theyre both together convert to Islam,they no need to remarried.
I pray for you,May Allah open his heart and bright his mind to accept Islam.
Subhanallah.