How do I wear a woman's three-piece business suit? Shirt required?

I recently bought a woman's Liz Claiborne three-piece suit. It came with a pair of trousers, a one-button jacket, and a third piece that I don't know what to do with.

It is a top that fits similar to a scoop-neck blouse, and it has a zipper down the side. It does not have sleeves, and it flares at the hips to create shape. All three pieces are black with a pink pinstripe, so it looks dark with just the three pieces together. Everything I've found online (general info about suits) says that it could be a vest, but I can't find my suit or anything like it displayed on a model anywhere online.

When I wear it without a shirt, it does appropriately cover my entire body (nothing risque), but I wouldn't take off the jacket because bare arms are not business appropriate. I could see wearing it with a button-front shirt under it without the jacket as cute office-appropriate wear.

So, should I wear a button-front shirt under the third piece when wearing the jacket?