All my kitchen cabinets have veneer on them. Is it possible to paint

Sure! Use a de-glosser first, so give the surface something for the paint to adhere to, then paint. Make sure you don't use matte finished paint, as it will be impossible to clean. Go semi-gloss or gloss.

here is a link that can give you some information

https://www.ehow.com/how_7705173_paint-over-veneer-cabinets.html

http://homeguides.sfgate.com/refinishing-veneer-kitchen-cabinets-36806.html

I have just finished mine and they look great. I wanted Matt look not gloss. Lightly sanded down with fine sand paper,then used exterior chalk paint (harder wearing and waterproof, great colours too) finished off with light waxing. Make sure you use a fine bristle very soft paint brush.

Yes, I painted veneer cabinets. If they are really dark veneer , and your going lighter, I would first use a primer. If your going darker no need too worry.