River help

[Chashio]

There are underground river systems in deserts. I doubt they would involve caves unless the desert was somewhat rocky/mountainous (of the right kind of rock), but I'm not actually sure on that. You might have your subterranean river sink into the sands of the desert, and as it hits higher bedrock near your forest it could pool into small lakes and then turn back into rivers on the surface that flow through your forests, while also eating away the bedrock in places underneath to create a cave system under the forest... they'd be filled with water, though, unless your creatures are sentient and crafty enough to seal off the cracks or the river takes a deeper path leaving the higher caves dry. You might do a search on subterranean rivers in deserts and see what options are already there. You might also like to investigate blue holes. Find out what types of rock are most likely for your scenario and see if you can work those in to suit your needs.

There's also the springs that well up in the mid-east of Australia, formed by an inland sea which left behind a layer of mud to seal off the porous sandstone underneath. Rainwater seeps through the cracks of the mud into the stone and then keeps that water from evaporating. Where the mud layer is broken the water pools up on the surface. Not quite what you want though, I think.