The business is an asset of the bankruptcy estate. If the business does not have any value, it may be protected, but if the business has value, it will be subject to turnover to the trustee. You should also make sure your corporate documentation is in order to properly reflect the proper ownership, but this cannot be done until after your boyfriend's case is closed. I suggest you schedule an appointment with a bankruptcy attorney so you understand your rights.
A Chapter 13 is likely the better option to protect everyone's interest in the corporation. He will be required to list any interest he has in the business and place a value on the business, which might impact the way he pays his creditors back. Typically, the bankruptcy should not impact the other owners in the business, and the renewal probably would not have a negative impact on the business. The petition will ask for information regarding all businesses owned within the last six years, so the business will be listed regardless of who renews.
Your boyfriend will likely have to provide the chapter 13 trustee with a business valuation prepared by a CPA or qualified business consultant. Hopefully, there is documentation establishing your mother's loan to the business and the fact that this indebtedness is still outstanding, as well as documentation that essentially all three of you are partners/equal shareholders. Since your mother has not been repaid, it would appear that the business has not been overly profitable to this point, and therefore its value, keeping in mind the indebtedness to your mother, should be modest. If the agreement between the 3 of you is mainly oral rather than in the form of written contracts and documents, then you should seek the advice of an attorney.
Your boyfriend can file chapter 13 to protect his home, and the business can continue to operate. Your boyfriend's interest in the business will have to be disclosed to the court and the chapter 13 trustee. A fair market value will need to be assigned to his ownership interest. If that is not readily available he may have to get a CPA or valuation expert to value it. If it has any value that exceeds any available exemption then it may impact how much he has to pay to his unsecured creditors in the chapter 13.