Is money deposited in banks in the form of a deposit, the profits of which are used for household expenses and children's education, halal?

If funds are deposited for Mudarabah (profit-sharing) in an Islamic bank that observes the rulings and regulations of Sharia, then this is permissible, and the profits are lawful. However, if the deposit is made in an interest-based (ribawi) bank, then this is not permissible, and the profits derived therefrom are not lawful.