I would not count mulch as soil.

IME peonies will not bloom if planted too deeply and mine are not fond of mulch. A sprinkle is adequate.

First, peonies are not bulbs :-) They have a fleshy root system emerging from a central crown. On the top surface of the crown should be several shoot points or eyes (usually white, pink or sometimes red).

These are what need to planted so that they are no deeper than 2" below the soil surface. And it is perfectly acceptable to cover with a couple of inches of light mulch.