Is it permissible to pay money as an intermediary to secure a government job for the husband, or to agree upon a monthly sum in exchange for that, knowing that he is competent and needs the job?

If the intermediary takes money for interceding for a permissible job, and this is outside the scope of his primary duties, then your husband is permitted to pay him the money, provided that your husband is qualified for the position and his employment does not prevent someone more deserving from being hired. However, if the employment falls within the intermediary's job duties, he is not permitted to take money, as it is considered a prohibited bribe, for the Prophet, peace and blessings be upon him, said: "The Messenger of Allah, peace and blessings be upon him, cursed the one who gives bribes and the one who takes them." An exception to this is if the husband is entitled to the job and cannot obtain it except through this means; in such a case, he is permitted to pay, and the sin falls upon the intermediary.