I have mutual funds and bank accounts in my name from inheritances. Are these assets counted by Medicare or Medicaid when seeking assistance for my husband with terminal dementia?

I would highly recommend talking to an attorney that specializes in Medicaid/Medicare or Elder law. Yours is a tricky situation because, even though your assets are in your name, you are still married and in some states those assets would be considered joint or community property.
Also, ask your attorney about a Living Trust. You can protect certain assets but you would need to appoint a "trustee" who will oversee whatever you put under the trust.
Could life get any more complicated??
good luck,
Lilli