I would imagine that cardboard might help retain moisture but it won’t protect the planter from rotting. I would use plastic.
You can use anything tough, old compost bags, pond liner, old tarpaulin. If you are buying in compost in bags use those if you have somewhere to tip it.You can buy nails with a broad head meant for nailing shed roof covering which would work if you don't have a staple gun or the copper sort for slate roof tiles
I think the idea for the sides is to stop water but for the bottom you need drainage.so even with weed membrane you will need some holes in the base.Your container will last a few years even without a plastic liner, then your husband can put his skills to use and make you another. 😁