Is it permissible for a woman to pray beside her husband, and what is the ruling on this according to the four schools of thought?

The Sunnah for a woman is to stand behind the Imam, not beside him to his right or left. This is a matter of consensus among the four schools of thought.

If she deviates and stands beside him, the Malikis, Shafi'is, and Hanbalis consider this disliked (makrooh), but it does not affect the validity of their prayers.

As for the Hanafis, they hold that it is not permissible for her to stand beside him, and the Imam's prayer becomes invalidated under certain conditions, while hers does not. The preponderant view is that of the majority.