It was most likely UF and is at least 12" (if protected by GFCI or 18" otherwise). The word you are looking for by the way is "ROMEX" a brand (and commonly used synonym" for NM cable which is NOT legal here.

If you're digging by hand, just be careful. Anything above 12" should be protected by conduit (or the extended length of the lamp post).

Posted by ronnatalie (My Page) on Mon, Jul 15, 13 at 8:42
If you're digging by hand, just be careful. Anything above 12" should be protected by conduit (or the extended length of the lamp post).

We are digging by hand.
The potted ball portion of the plants/flowers are about 8-9 inches.

So are you okaying the dig for anything above 12"?

Or should I just nix the idea altogether?

You know the trench location from the house to the pole. If you are not sure about depth, simply don't plant anything directly above the trench.

you've already placed a planter and planted shrubs over the trench from the looks of it.
Why all the sudden now are you worried that you're going to hit the cable?