Can my ex-husband kick me out of the house that we both own?

You don't really provide enough information about your situation to be able to answer your question. Generally, if you are a joint owner, your rights with respect to the house are the same as any other owner's rights, unless your ownership share is smaller, or there is a contract, agreement, court order or other legal document that provides otherwise. If he is your ex-husband, it is unclear why you both still own the house together, but you should speak with an attorney to clarify what your rights regarding the house are.

It depends upon what happened in the divorce and whether there is a rental agreement, or perhaps an ejectment action. Yes, he might be able to get you out of the house.

If you both own the home and are currently living there, I am not aware of any statute that would allow one owner to kick out (evict) another owner. The question that comes to mind however, is 'was this situation covered in the divorce judgment? and if not, why not?

No, if you are on the title you have the right to stay there until a judge says otherwise.