It is all legal. Just don't lie about your status. Tell the lender that your a refugee (asylee is not all the time well known). Be ready for more questions, clarification and explanation. But yes, if you could pull a loan in your asylee satus it is all legitimate and totally legal. you are entitled to live indefinitely in the USA (that could be seen in one hand as permanent residency).
Go ahead and invest don't hesitate.
Best Luck.
