In short: Good news, no cancer, keep an eye on it though.
My follow-up visit at the dermatologist was this morning, and the results are back. I don't have cancer, BUT the slides were "very abnormal" and I should have them checked out again every year. I don't know if this means they need to be biopsied every year or just examined, but I'll go back next January anyway.
What was abnormal about the biopsy? Well, there was a significant amount of "atypical fibrosis" just under the epidermal layer of skin. Basically, that means that there are a lot of pre-differentiated cells that have no real purpse except to divide and make more cells. After the cells divide, some of them differentiate into specific tissue type, in this case, skin epithelial cells. Except I have an extra patch of these cells in both the moles on my back, and this can eventually turn cancerous if they start growing out of control.
Luckily, this type of cancer, if it does develop, is fairly easy to treat by removing all the cancerous tissue which will leave me with a hole in my back and some stiches. It should heal nicely and I will have no other ill effects hopefully. But it hasn't come to that yet.