Can my husband apply for my parents and can I be a co-sponsor after getting my green card?

There is no visa category by which a U.S. citizen may petition for a mother-in-law or a father-in-law, or by which a Permanent Resident may petition for parents. You mentioned that your parents are legal to work in the U.S., but you did not mention their current nonimmigrant visa status. There really is no substitute for your family to consult with an immigration attorney who, after learning all of the relevant information about your family members, could advise about potential immigration eligibilities, options and strategies to attain your goals.