I'd line the entire thing with plastic - esp.if you don't know what the wood may have been treated with. If the box is poplar or pine (as many pallet forms are) it will rot pretty quickly from the moisture. Alternately, you could seal the wood with melted beeswax to waterproof it & reduce the chance of anything leaching into your soil.
Well, Hubby and I decided to wrap it in plastic about half way up and paint the wood next spring or whenever we get the extra money, hours have been tight at work so the checks have been lacking. But for now it is upside down with black plastic over it and my potted plants on top, so it is doubling as a tabble and hidey spot for my strawberry boxes that I haven't planted yet but will get started next spring in my huge garden planing spree. Got some holes drilled in one of my big pots so I can actually plant something in it next year, which is going to be an insulator for my Christmas tree this winter so it can be planted next year. So many plans that have to wait yet again, I'm scared to get the pallet box filled with dirt and herbs and have to move them next spring and have the whole box give out. Going to see if maybe my neighbor will house my blueberry plants in his greenhouse over the winter since they haven't been planted yet and are still in the nursery pots. Our winters aren't snow hard, but I am scared of a repeat super low temps killing plants that should have survived. Going to see if Grandpas will let me plant (10)"a couple" blueberry bushes around the front yard spicket where the pine tree has been dropping needles for the last 15+ years and finally died, which is also where I would like to plant my Christmas tree once we get the old one chopped down. If he wont let me plant them there I am going to have to hope for some good pots to plant them in at the new place. But that is also just my ideal number of plants to add to my 2 blueberries I have already have, I have a case of the garden math kicking in.