Is it permissible to live with a husband who takes out a riba-based loan?

If the loan that he has asked for is halaal, i.e. it is not based on riba, and he intends to pay it back, then there is nothing wrong with this, and this is not regarded as a sinful loan. 

But if this loan is a riba-based loan, then it is haraam and it is not permissible for him to take it or to start a business with this haraam money. 

“And whosoever fears Allaah and keeps his duty to Him, He will make a way for him to get out (from every difficulty).

 And He will provide him from (sources) he never could imagine”

[al-Talaaq 65:2-3]

and :

“Whoever gives up something for the sake of Allaah, Allaah will compensate him with something better than that.” 

If you want to advise him, then in Question no. 9054 you will find some comments on this topic which you can give him so that he might benefit from that, and avoid that which is haraam.  

With regard to his consuming riba, this may be grounds for you to ask him for a divorce (talaaq) or to ask for khula’, but you do not have to do that, rather it is o.k. for you to stay with him and live with him whilst continuing to advise him to do that which is better, especially if there is the hope that he will mend his ways. 

With regard to eating from his money, if he has a permissible source of income other than this, then there is no sin on you or on you children if you eat from this money. But if all his earnings are haraam and you cannot find any other source of maintenance, and you have no other halaal source of income, then it is permissible for you to take just what you need, and no more, because Allaah says (interpretation of the meaning): 

“So keep your duty to Allaah and fear Him as much as you can”

[al-Taghaabun 64:16]

So in this case if you take money, you are taking what he is obliged to spend on you. But you should still continue to advise him and tell him to refrain from taking haraam loans, and to look for a way that is acceptable according to sharee’ah, so that he can do work and earn his provision thereby. 

And Allaah is the Source of strength.