I'm glad that you posted about your husband's problems with falls. This sounds like it must be a difficult problem for both of you. Falling certainly increases his chances for injuries that could put him in a facility, rather than staying at home.
I would agree with @colleenyoung that, you probably need to get him to a doctor's appointment, either in person or virtual visit, and explain the problems with falls. He might make an adjustment in his Sinemet which could be helpful.
When he falls is it several hours after taking a Sinemet? If so, this could represent what is referred to as "off-time." This is the time when the Sinemet isn't working as effectively. Perhaps an increase in the dosage or an increase in the number of meds might be suggested by his doctor.
I understand the problem of getting people to use assistive devices like walkers. It will often be met with resistance. Perhaps his doctor could talk with him about the importance of using a walker so that he does not fall and risk breaking a bone or having a head injury.
Will you try to schedule an appointment where you can both talk to his doctor?