Automated huh... hmmm.. Two ways I can think of.
The easiest thing to do is to use an action to apply the filter on a layer by layer basis. But as you've discovered, the caveat is, if you want it automated, all PSD's containing these multiple layers, must have A) the same number of layers and B) they must be the same name across all PSD's. In other words, layer 1 has to be the same name in all your PSD's, layer 2, etc.
If they don't have names other than your standard Layer 0, Layer 1, Layer 2, etc., it's do-able, but condition "A" above applies.
That's messy and icky.
Another way, and I've never tried it, but it goes like this: save out each layer as an individual PSD. There's an action to do it here <http://www.adobeevangelists.com/photoshop/actions.html>.
Then you create an action to run the filter on one image.
Next you File|Automate|Batch and run that Filter Action on the folder containing the individual PSD's that were saved.
Crimoney... this won't work - there's no way to reassemble the individual PSD's automagically. I considered deleting this since I can't figure out how to marry all the layers back together again, but decided to keep in the post in case someone else can think of a way, or perhaps it inspires another idea.
The long and short of it, is that it's a PITA, any way you slice it.