I am not sure what type of mulch it is especially as you say it is not wood chips or sawdust. Could it be a compost mulch? From the image you sent it looks like it is weed free compost. If so, you could lay sod right on top but it would be much better to mix the mulch into the soil down at least six inches so that there is not a layer of soft mulch then a layer of hard packed subsoil. You want the grass roots to travel deep into the soil not stop once they get past the soft mulch and hit the hard soil below. You may want to bring a sample of this mulch to where you purchase the sod  and get an opinion from the professional sod grower. Keep growing, Marianne Binetti