I make a lot of tri-lams, mostly heavier poundage ELBs and warbows. I use ash, hickory, maple, and elm as backing material, and I've used purpleheart, bloodwood, greenheart, bamboo, jatoba, and maple as mid-lams, and they usually end up being the same thickness at 1/8".
For belly wood, I usually use osage, and ipe, but also lemonwood and jatoba. The belly wood thickness will end up being whatever thickness is required to make draw weight, usually between 3/4" - 1". If you make the lams too thick, the belly wood may disappear at the tips.