This ferry was run by Jadrolinija last summer but it's unclear whether the ferry will run this year. There is another passenger ferry from Split to Milna and Hvar that goes on to Vis island.
The timetable clearly doesn't allow much time in Milna or Hvar! There is the option to take a later car ferry back from Stari Grad to Split. Also take a look at the seasonal Split-Brac-Hvar-Korcula-Mljet-Dubrovnik catamaran. See below for all ferry options.
Another option is to take a day tour to Hvar Island from Split.
You can buy tickets online at the Jadrolinija website or at any local travel agency.
Car Ferries (All run by Jadrolinija)
Split-Hvar-Vela Luka-Lastovo Jadrolinija