As naught already mentioned, I find it unlikely a specific name for the type of chart is currently in use, although just identifying it by its common components with other charts (a line chart and an area chart superimposed) I would think would be sufficient.
Essentially when working with any statistical program that can produce statistical graphics, the graphical elements of the chart (lines and area) can be added to a plot in a programatic fashion, as well as rendering the cartesian coordinate system. The other meta data elements though (labels for lines and area fills, the background Calm and Segregate Arrows), are unlikely to be implemented in a programatic fashion. This is because they aren't data in the sense that their coordinates, orientation or any other aesthetic in plot directly depict data, hence their placement within the chart is arbitrary.
In my experience typical meta data that can be automatically added to plots are axis labels and labels for graphical elements (and labels for the axis that define the cartesian coordinate system obviously). Placement of labels to avoid overplotting of graphical elements is very difficult though, and so I would bet the labels in the above chart were placed by hand in a vector graphics editing program (like illustrator). You could do it programatically, but it would only work for the one particular chart you taylor it to.
The supplemental labels for the Y axis guide is unique, and so such a guide is unlikely already implemented in any statistical program (although in theory that would be much easier to implement than placement of the labels for elements within the plot).
IMO there isn't much point to adding a name to a particular type of chart once you understand the grammer of the components that make up the chart (which you do given your question). Knowing the grammar there could be very many different types of charts, and so what is the point in giving a line + area chart a special name.
It would be possible to make such a graph in excel (I don't know about Matlab), as well as various other statistical programs. Although it would be difficult to whip up a turn-key script to produce such a polished graphic as the one posted in your question (compared to the amount of time to add such elements post-hoc in a vector editing environment).