Soak figs in red wine for 30 minutes. Preheat oven to 350°.
Season chicken thighs with salt and pepper. Heat a large sauté pan, add olive oil and butter and sauté chicken pieces until brown on all sides. Add bay leaves and 2 tablespoons of water, cover and transfer to preheated oven. Baste every 10 minutes, until the chicken is cooked, about 30 minutes. Keep oven on.
Remove figs from the red wine and cut in half lengthwise. Arrange the figs in a small baking dish, add 4 tablespoons of soaking liquid and bake 10 minutes. Reserve remaining soaking liquid.
When the chicken is cooked, transfer the pieces to a platter and keep warm. Discard bay leaves. Pour out all but 2 tablespoons fat. Add vinegar, honey, remaining red wine from figs (from baking and soaking liquid) and chicken broth and bring to a boil; reduce to about 1/2 cup.
Add olives and heat just to warm; spoon sauce over chicken and surround with figs. Garnish with chopped parsley.