Is it considered permissible or impermissible for a husband to agree to an offer from a company that requested to benefit from his expertise in exchange for a percentage of the profits, to help them secure a project that his own company is supervising, knowing that these profits will settle their debts and provide them with a comfortable life?

Your husband is not permitted to provide information to a company participating in a tender that would enable it to submit the best bid in exchange for a percentage of the profit. This constitutes a breach of trust, taking a bribe, and injustice to other companies, even if he does not take money. This percentage he takes is considered a forbidden bribe in exchange for disclosing what should not be disclosed. Furthermore, it is not permissible for him to work as a partner with the entity entering the tender in exchange for a percentage of the profit, as this contradicts his work and compromises his integrity. He must fear Allah and perform his work honestly, and not accept any gift or profit.