Will using dry lube and wet lube together give you better protection/performance than from using just one of them?
I don't think so - they are designed to be used individually, and for a specific purpose.

Like I answered to a previous question, the Wet / Dry naming of the product is a hint as to what conditions the product is designed for.

Wet lube is typically more like motor or sewing machine oil, and is designed to coat the chain and protect it in wet conditions. This will pick up dirt and gunk, but it will be mostly kept on the surface and will help keep water and other corrosive substances out of the links.

Dry lube is usually a teflon lube in an evaporating or wax base, so the teflon particles stay in the links without a lot of wet "gunk" left on the chain to pick up sand, dust, grime, etc. and is great for dry, dusty conditions.