In the (Muslim) RE classes I endured, there was no mention of Mohammad's jealousy as the reason behind the hijab.
It's been two decades since I read the Quran, but what I remember from the context is that that thieves were attacking vulnerable persons, women in particular. God told Mohammad that to avoid this, women should cover 'their adornments'.
This is interpreted in a quite fascinating manner by some who argue that all that is beautiful about a woman (her eyes, mouth, body) are her 'adornments' and should thus be covered up.
"O Prophet! Say to your wives and your daughters and the women of the faithful to draw their outergarments (jilbabs) close around themselves; that is better that they will be recognized and not annoyed. And God is ever Forgiving, Gentle."
and
"And say to the faithful women to lower their gazes, and to guard their private parts, and not to display their beauty except what is apparent of it, and to extend their headcoverings (khimars) to cover their bosoms (jaybs), and not to display their beauty except to their husbands, or their fathers, or their husband's fathers, or their sons, or their husband's sons, or their brothers, or their brothers' sons, or their sisters' sons, or their womenfolk, or what their right hands rule (slaves), or the followers from the men who do not feel sexual desire, or the small children to whom the nakedness of women is not apparent, and not to strike their feet (on the ground) so as to make known what they hide of their adornments. "