Good question.
Nowadays, the only conversion to Judaism which is done according to Jewish law is the Orthodox one. According to Orthodox (or traditional) Judaism, the center of Jewish life is not the synagogue, it is the home, the family. Thus, a woman cannot convert to Judaism if her husband is not on board with it, since a Jewish home takes both partners...
Conservative and Reform congregations do not follow Jewish law, and they basically make up their own rules. Thus, they would accept anyone under any conditions.