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It appears you are using Tableau 7.0. In Tableau 7.0, all you need is one continous (green) date pill and you can drill down without lines. Drilling up is a bit more difficult, you need to right-click on the pill and choose the higher-level date from the context menu (if there's an easier way to drill up, I haven't found it). Make sure to choose from the second set of dates in the context menu, those are continuous dates.
Here's a bit more about continuous dates from the Tableau documentation: http://onlinehelp.tableausoftware.com/current/pro/online/en-us/dates_continuous.html
Thanks for your info.