What can I do to prevent injury to my husband who is now unstable?

Depends . Depends on the cause, degree and type of instability. Needs fall safety evaluation and would make appointment with a physical therapist physician.
Falls? I am assuming you are stating that your husband falls over, not that he is emotionally unstable. Removing throw rugs, small tables, getting adoptive equipment in the bathroom and kitchen, a ramp next to the stairs... Have a home safety inspection will help pinpoint what you and he need to get by at home.