All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
According to your question, your husband contradicts the Sharee'ah since it orders husbands to kindly deal with their wives – as Allah, the Almighty, says (what means): {… And live with them in kindness.} [Quran, 4:19] Kind treatment includes satisfaction of the wife’s emotional and sexual desire. On the other hand, you have taken an evil path through establishing such heinous emotional relations, maintaining that your husband’s unfulfillment of your rights could in no way justify such relations or the commitment of such immorality. As such, you are now disobedient to your Lord and do not duly fulfill your husband’s rights. So, you have to hasten to sincerely repent to Allah.
Also you have acted wrongly by telling your husband about such relations, rather you were supposed to conceal your sin along with repentance. As for the attribution of your children, the original ruling is that they should be attributed to your husband unless he denies them through Liaʿan. Besides, according to the International Islamic Fiqh Academy decision, DNA profiling is not permissible be used to deny paternity.
Concerning your husband’s inclination to homosexuality as you mentioned in your question, if the matter is still mere inclination without committing this heinous immorality, you should show patience with him and help him to do his best to ward off such evil whims. However, if he had already committed this crime, he has thus involved himself in big danger, and thus you should remind him of Allah and His Severe Punishment. If he repents to Allah, you have – praise be to Allah – achieved your goal; otherwise, we advise you – under this very case – to attempt to be divorced from him. Yet, if he responds positively to your request, that would be fine; otherwise, you should report your case to an Islamic Center.
Allah knows the best.