You can file individually if you choose even though you're married, however the non filing spouse will not get the benefit of the discharge and will still be on the hook to the extent they were before the other spouses bankruptcy filing.
Mr. Larkin is licensed to practice law in CA and is located in San Diego. His response here does not constitute legal advice and does not create an attorney/ client relationship. The response is in the form of legal education and is intended to provide general information about the matter in question. Many times the questioner may leave out details which would make the reply unsuitable. Mr. Larkin strongly advises the questioner to confer with an attorney in their own state to acquire more information about the specifics of their case.
Regardless of the state you are in, you are never required to file bankruptcy with your spouse. I cannot answer your foreclosure question because I am not licensed in Texas and the answer may depend on laws unique to Texas.