Q. I converted to Islam. My husband respects my decision. I was told that if I do not convert him than I am not a muslim anymore.
A. May Allah keep you guided as well as the rest of the muslim Ummah, Ameen.
Msulim woman are only allowed to marry and be married only to Muslim men. In the case were a woman converts to Islam, the husband must be presented with an invitation to Islam. The two general opinions are as followers:
Her conversion to Islam immediately negates her marriage to her non-muslim husband.
The Ahnaf are more lenient. They state that upon her conversion, Islam must be presented to him. It would be preferred that Islam be presented to him by a person that is qualified enough to help bring clarity to any resistance he may have pertaining to Islam. His acceptance during the Iddah (waiting) period resumes the marriage as normal. His acceptance of Islam after the Iddah period would call a renewed nikah.
His refusal to convert under general circumstances would not negate your faith. It would make you be a transgressor. Bearing children from such a relationship would cause for the children to be islamically illegitimate. There would be many other negative consequences as well causing you to be part of a sinful relationship.
It is best you take this matter to your local scholar with husband in hand, so as to resolve this matter in a time efficient manner.
Allah Certainly Knows Best.