Doubleheaders are rare in baseball these days; few teams schedule them (the A's were the last to do so, in 2011; that was the first scheduled DH since 2003), so they're generally played only when games are postponed for inclement weather.
Arizona's first home doubleheader is a result of a scheduling snafu. The Diamondbacks (62-61) were originally slated to play games on 23 consecutive days, which is a violation of the basic agreement between the owners and players. So in early August, the league turned Wednesday's game into a doubleheader, providing Arizona with a day off Thursday.
The Diamondbacks have played 10 doubleheaders on the road in their 15-season history: two in Colorado, Philadelphia and New York and one each in St. Louis, Chicago, San Francisco and Florida. They've swept two, been swept twice and split the other six. Naturally, so as not to lose revenue, Wednesday's is a split-admission twin bill; the rescheduled game is in the afternoon, with the regular game following at night.