Just like with a glass bow tri-lam bows have to be engineered as far as what materials used for which lam to go along with your bow design. Of course you want tension strong backing material and compression strong material for the belly. The core is important too so you will want a core that has strong shear properties, is light in physical weight and takes glue well.
You could start with a 1/8" backing. Both boo or hickory fit that bill(as do other woods). For compression strong woods, osage, yew come to mind although there are others. I'd go a bit thicker for the belly lam because that is where most of the wood removal comes from while tillering.
For cores probably hard maple, ash, elm, and others will work and probably 1/8" there will be plenty.
When dealing with an all wood tri-lam you are dealing with natural materials and consistency is hard to come by with natural materials unlike with a glass bow.