Is there a way to find out if your husband filed a living trust on home and property without the spouse knowing about it?

A Trust funded by real property (e.g., home) should have some Trust-related document (generally giving some brief information about the Trust) and a deed showing the Trustee(s) owning the property recorded with the Recorder for the County in which the real property is located. The Recorder or a real estate agent/broker will help you with your search which you can begin and maybe conclude online. I have no comment about a trust as to the inexcusably vague term "property".

Yes there is a way to find out is property has been put into a trust. This requires an attorney such as this firm, or some other person who has access to public records. You cannot just do an internet search and obtain this documentation. This is a service we provide to our clients regularly.