Is it permissible to take out an interest-bearing loan to face financial hardship, represented by the husband's lack of suitable employment and the need for money to cover living expenses, education, and a program development project that may improve income?

It is not permissible to borrow with interest (riba) except when there is a necessity that permits the forbidden (haram (definition)). This necessity is defined as a strong likelihood of a person falling into perdition, or facing unbearable hardship, or being unable to secure the minimum standard of living for the poor. The reasons mentioned [in the question, though not provided here] do not permit borrowing with interest. The husband must seek lawful means of earning. Satan may close paths and beautify the forbidden.