I would not call these a mustache handlebar; a mustache bar has larger flatter curve as the bar bends back toward the rider with less flair. Most mustache handlebars are designed around different hand positions including the ability to place brake levers on the front of the bar as below.
I'm not sure the correct name for your bars, I call them 3 speed bars, but I've also heard them called Townie bars. Those bars are currently made by the retro bike sites such as Nitto (Rivendell) and Soma and I think Velo Orange who have their own names for their particular model.