While it was probably harder for me than Herb can imagine, I think I finally
figured it out.

Try:
Sub ApplyNewStyleBetweenTweUniqueStyles()
Dim oRng As Range
Dim oTempRng As Range
Set oRng = ActiveDocument.Content
With oRng.Find
 'Look for the Heading 2 text on execute
 .Style = "Heading 2"
 .Wrap = wdFindStop
 While .Execute
   'Collapse oRng to end of found Heading 2 text
   oRng.Collapse wdCollapseEnd
   'Set a temporary range that starts at end of Heading 2 text
   Set oTempRng = oRng.Duplicate
   'Look for Heading 3 text on execute
   .Style = "Heading 3"
   .Execute
      'Collapse oRng to start of Heading 3 text
      oRng.Collapse wdCollapseStart
      'Define temporary range that ends where Heading 3 text starts
      oTempRng.End = oRng.End
      'Apply style
      oTempRng.Style = "MyStyle"
      'Set execute to look for Heading 2 text
      .Style = "Heading 2"
   Wend
End With
End Sub

Where "MyStyle" is the name of the style you want to apply.