Can married couples hold property?

Yes. After marriage, there are many ways of owning property. They differ from state to state.

Sole tenancy, which is when one individual has ownership. The property is passed on in accordance with the will at death.
Joint tenancy, with the privilege of survivorship. Two or more people have equal ownership. The property is passed to the joint owner upon death. This should be used to effectively avoid probate.
Tenancy in common, property has joint ownership with the privilege of survivorship. The property is passed on according to your will upon death.
Tenancy by the entirety, like joint tenancy, with privilege of survivorship. This doesn’t allow a spouse to get rid of the property without the other’s consent and is only possible for spouses.
Community property, property that is gained through marriage that has equal ownership. States such as AZ, CA, ID, LA, NV, NM, TX, WA, and WI allow community property.