How can I refinish our paper kitchen cabinets?

If the paper is NOT in horrible shape or pealing off , you can certainly paint over it. Just clean them really well with TSP or some other heavy duty degreaser and apply a coat of primer, than some cabinet paint.

Here is a video on how I painted my bathroom cabinets. Do not use the deglosser on your cabinets, since they may damage the paper and ruin your work. Just make sure they are clean and dry before applying your primer and paint. Good luck!

https://youtu.be/Ko5CsLqNIZQ

Take one of the cabinet doors or drawers to the paint department of your home improvement store and see what they recommend. They have the best paints and application tools for a professional job.

As long as the coverings are still in good conditions - no buckling, bubbles or splitting... you can paint it with chalk paint.

I would start with an oil base primer.

I think I have same problem you are andI found a post about the wood look fronts are peeling off and the lady took the doors off and laid a wash cloth on the door and used her steam iron to get it to peel up the rest of door then lightly sanded them restain them and seal them I'm getting ready to try to do the same thing I'll try to post when I get mine done