Is it permissible to register the house in the name of the husband's brother so that it can be rented out through the husband's work and the rental income used to pay off the loan, knowing that the husband's employer will deduct the rental allowance from his salary?

It is not permissible for your husband to defraud his employer by telling them that the house is not his, when the opposite is true. This is deception, and whatever is taken from them based on it is consumption of wealth unlawfully, due to the Prophet's (peace and blessings be upon him) saying: "Whoever deceives us is not of us," and due to Allah's Almighty saying: {And do not consume your properties among yourselves through falsehood}. However, if he informs the employer and they agree to it, then there is no blame upon him.