My requirements:
You could use two stages, but for your case it would be better to just solve this problem by creating two groups inside a single stage:
Stage stage = new Stage();
Group background = new Group();
background.setBounds(0, 0, Gdx.graphics.getWidth(), Gdx.graphics.getHeight());
Group foreground = new Group();
foreground.setBounds(0, 0, Gdx.graphics.getWidth(), Gdx.graphics.getHeight());
// Notice the order
stage.addActor(background);
stage.addActor(foreground);
foreground.addActor(new Actor());
// Or anything else you want to add like you normally would to the stage.
background.addActor(new Image()); // your background image here.
Gdx.input.setInputProcessor(stage);