Raised beds could be a solution, especially for perennials and small shrubs. You build low walls to create a large planter and fill it with soil. I made a nice raised bed out of concrete rubble once. Don't make the beds too big, though, it takes an amazing amount of soil to fill them. Do an internet search on "raised beds", you'll find good instructions.

To plant trees, though, you'll need to dig out the soil and figure out what's under there. Trees need plenty of root room and soil depth so they can anchor themselves and not fall over onto your house.

Personally, I'd dig out the soil a little bit to figure out what's under there before doing anything. You don't want to put a huge raised bed over something you might need access to later, like a septic system hatch.

That's really good advice that Carol gave. Definately find out what's down there before burying it!
You never know, according to Murphy's law if there is even one big rock buried over there then chances are that's where you just tried to dig..... maybe it's not as bad as you think?
I was pleased to find a few big buried rocks when digging in my own garden. I went through the trouble of digging them up and now they make nice accents in my yard.

But.... My inlaw's yard is a layer of topsoil and then fill underneath. When you dig the first 6 inches of topsoil it's great, but the subsoil is like a layer of rock. I end up chiseling out as much as I can and planting everything shallowly. Eventually I hope worms and organic matter will work down and break it up because there is no way short of bringing in a jackhammer that I'll ever make a serious dent in it.
Raised beds would be the way to go.

I think what I have pictured in my mind will be hard to put down in words but...

Try treating that solid layer of rock/rubble that is 6" down as your new "ground level". In other words, lay out some paths in your side yard. Then dig down to rock layer where you laid out those paths. Dig the paths a little wider and lay down your walls for the raised beds. Put all that topsoil you just removed onto the new raised beds. It may not add a lot but you may gain a few inches which will save on buying topsoil.

Did that make sense?

Also, once you determine it is not a septic tank or bomb shelter or something else you may want to get to some day, take a bar or shovel and just keep testing the ground every few feet to see if you can find any loose spots. Where you find your loose (or looser I guess) spots dig the holes for those plants you bought that have deeper roots. then place those plants with shallower roots around those.

If it is rubble and not bedrock I would try and find out how deep it goes. It is possible the builder just dumped rocks there and then graded over them.

Just some thoughts.

good luck, Jim

Thank you for all the good advice. After reading everything I went back today and began digging in earnest. There is a layer of rock there, but it isn't as solid as it first appeared. It's going to be a bugger to get through, but I do believe they are more a huge layer of small stones than one gigantic boulder. Still, this project may take a few years. Thanks again for all the help! :-)