I own a stock that is in both our names but my son is listed the beneficiary. Would that count as a asset?

If you or your spouse is filing for Medicaid, then yes, the stock will count as money.

The stock might need to be sold and "spent down". You cannot give it to your son, the money has to be used for you or your husband's care. Now, when it comes to Medicaid, the spouse is allowed to keep a certain amount if the spouse isn't applying for Medicaid, you would need to check with your State rulings.

If you and your husband are the owners of the stock, yes it cunts as an asset. The beneficiary has no rights to the asset until both of you pass.