Direct Burial Data cable
There are no rules stating you can or cannot use any type of ethernet cable with UF wire. Technically, you can just lay ethernet cable on the ground, under the ground, or drape it from the trees. Keep in mind that if you don't protect your wire, it will degrade over time.

I'd recommend using a conduit with ethernet cable, buried at a reasonable depth and sealed at each mating point with pipe cement. You cannot run line voltage in this conduit, just so you know, but will be future proof if you want to add another line or use coax or fiber.

The UF wire you're talking about would be for carrying power and should be installed according to electrical code, probably 18" below grade. It would also require connections be made on either end for supplying and using the power.