A denial of a STEM 17 month extension does not provide for an appeal. For your husband, he needs to become a US Citizen first before he can quickly file a green card for you and it takes about 4-5 months to get your green card once he naturalizes and that process can also take 4-5 months. If your STEM extension is denied than you could change status to B-1/B-2 visitors visa to buy you sometime. The B-2 doesn't allow you to work but at least you can stay here for approximately 6 months most of the time and try to apply for one additional extension but its usually very difficult to get another extension beyond the 6 months. When is your husband eligible to apply for naturalization will give you a timeframe of how long things will take and how you need to arrange time for your own status.
I agree with Mr. Calehr
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I agree with my colleagues
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