Is it permissible to continue the marriage to an atheist man who spreads atheism among the children and watches pornographic websites?

If you married this man while he is an unbeliever (kafir), then your marriage is invalid, according to the Almighty’s saying: "And do not marry polytheists until they believe." You must separate from him immediately. However, if you married him as a Muslim and he then apostatized from Islam, if he repents before the end of your waiting period ('iddah), then the marriage remains valid. But if he does not repent until your 'iddah ends, then the marriage is dissolved from the moment of his apostasy, and you must separate from him.