Can my husband have his home care with a personal assistant of his choosing instead of a home care company?

Sure. He can hire anyone he wants, if he is paying for it.

Is he on Medicaid? If they are paying, there are rules that must be followed, but in most states there are options. In Minnesota my brother was able to provide services to our Mom paid for on a Medicaid Waiver. They simply had him go through one of the agencies they use.

If your husband is on Medicaid, then the person to contact about this is his case worker. Find out what his options are and how to exercise them.