He wasn't cured of the curse, Melian simply opened his eyes.
What Morgoth did to Hurin was this:
Therefore Húrin was brought before Morgoth, for Morgoth knew that he had the friendship of the King of Gondolin; but Húrin defied him, and mocked him. Then Morgoth cursed Húrin and Morwen and their offspring, and set a doom upon them of darkness and sorrow; and taking Húrin from prison he set him in a chair of stone upon a high place of Thangorodrim. There he was bound by the power of Morgoth, and Morgoth standing beside him cursed him again; and he said: ‘Sit now there; and look out upon the lands where evil and despair shall come upon those whom thou lovest Thou hast dared to mock me, and to question the power of Melkor, Master of the fates of Arda. Therefore with my eyes thou shalt see, and with my ears thou shalt hear; and never shalt thou move from this place until all is fulfilled unto its bitter end.'
Morgoth eventually released Hurin himself (Melian had no part in that), but he was released into the world knowing what Morgoth wanted him to know and thinking what Morgoth wanted him to think. He wasn't magically compelled to believe these things, it's what he had been led to believe by Morgoth's visions and manipulation.
Unhappy was the lot of Húrin; for all that Morgoth knew of the working of his malice Húrin knew also, but lies were mingled with the truth, and aught that was good was hidden or distorted. In all ways Morgoth sought most to cast an evil light on those things that Thingol and Melian had done, for he hated them, and feared them. When therefore he judged the time to be ripe, he released Húrin from his bondage, bidding him go whither he would; and he feigned that in this he was moved by pity as for an enemy utterly defeated. But he lied, for his purpose was that Húrin should still further his hatred for Elves and Men, ere he died.
All Melian did was show and convince Hurin of the truth of what had occurred:
Then Thingol looked upon the great treasure, and knew it for the Nauglamír, and well did he understand Húrin's intent; but being filled with pity he restrained his wrath, and endured Húrin's scorn. And at the last Melian spoke, and said: ‘Húrin Thalion, Morgoth hath bewitched thee; for he that seeth through Morgoth's eyes, willing or unwilling, seeth all things crooked.
Long was Túrin thy son fostered in the halls of Menegroth, and shown love and honour as the son of the King; and it was not by the King's will nor by mine that he came never back to Doriath. And afterwards thy wife and thy daughter were harboured here with honour and goodwill; and we sought by all means that we might to dissuade Morwen from the road to Nargothrond. With the voice of Morgoth thou dost now upbraid thy friends.
And hearing the words of Melian Húrin stood moveless, and he gazed long into the eyes of the Queen; and there in Menegroth, defended still by the Girdle of Melian from the darkness of the Enemy, he read the truth of all that was done, and tasted at last the fullness of woe that was measured for him by Morgoth Bauglir.
Hurin was not freed from a spell, he was simply told and shown Melian's side of the story, and knowing Morgoth, he understood that by being deceived by Morgoth he had only served Morgoth's will. At that point, still under the curse, he kills himself.