He married her in order to forget his ex-fiancée; and the ruling on correspondence between the sexes
Allaah has made marriage one of His signs, and has created love and compassion between the spouses, and He has made each spouse a garment for the other. The basic principle regarding marriage is that it should be lasting: it is not permissible for either spouse to go against the purpose of marriage. Your husband should have feared Allaah and had a good intention before embarking on marriage. So long as he married you with your consent and all the conditions of marriage were fulfilled, then your marriage is valid and there is no doubt about it.
It is also haraam for him to establish relationships with women who are “strangers” to him [i.e., non-mahrams] and to correspond with them, so how about if that correspondence also involves obscene words such as words of love and romance? See the answer to question no, 23349.
With regard to yourself, why don’t you speak frankly with your husband and advise him? That may bring him back to his senses. Or you could ask some good people to intervene and advise him.
If he cannot forget her, then it is permissible for him, according to Islam, to marry her if she is a kitaabi [one of the People of the Book, i.e., a Jew or a Christian], subject to the condition that he repents from having had haraam relationships and he comes back to being chaste.
In that way he will protect himself from falling into haraam actions. Allaah permits Muslim men to marry chaste women from among the People of the Book (Jews and Christians).
You have to be patient and not hasten to separate from him. Perhaps if you stay with him and are patient with him, and keep on advising him, that may be the cause of his being guided and coming back to his senses.
If he insists on separating and continuing to do haraam things, then you should not feel bad about it and should not be keen to stay with him. Whatever the case, we ask Allaah to guide us and you and him and give us strength.
And Allaah knows best.