Why put property in someone else’s name?

If your husband is truly the trustee, he does not own the property: a trustee manages a trust, but the assets or property are owned by the trust itself, not the trustee. (This is similar to how to a store might own the land it occupies, and the stores general manager may manage the property, but does not own it.) A trustee is not liable for the property in the trust simply by virtue of the property being there; he'd only be liable if he actually does something wrong with or in regards to the property.
Therefore, this property should not be coming up or showing as owned by your husband or being in his name: it should be in the trust's name. If it's in your husband's name, he IS the owner and so would be liable for it.
As to why someone might put property in another person's name: if he is trying to hide it from creditors, from a child (e.g. child support), from a spouse or ex-spouse (alimony), from the government (taxes or Medicaid); or he is doing something illegal with it and doesn't want it connected him. While there are legitimate reasons to put property in a trust, so avoid probate in the future, or to give another person the benefit of it without actually giving it to them (e.g. if you don't trust them to manage their own money or property), or sometimes for tax benefits, there is really no good reason to put it into another person's individual name unless you are simply gifting them the property (like a parent might give property to a child).
Also, you can't legally be made owner or trusteewithout your consent.
Something odd may be going on. Retain an attorney to help you figure it out and, if necessary, do something about it.