Creating hybrid EditorKit which can alternate between for example markdown and source-code

Question

Say I have an EditorKit for CSS styled Html (SwingBox), and I have an EditorKit for source code (SyntaxKit). Can I create a synthetic editor kit for a JEditorPane that combines these two, so that I can have interleaved HTML (which would come from a markdown parser) and source code (handled by the SyntaxKit)?

E.g., like shown below. Note that I do not want to render the source code via a markdown-to-HTML parser, but use the specific syntax kit with its own lexer.

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And here we have some literal programming stuff. With images etc.

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object Foo {
  def bar = 1234
}