If a control, like a button is inside a combobox by using a cellfactory, is clicked. It doesn't respond to the events. So, if we have an scenario like the following, events won´t be triggered. There is no possibility to develop complex cells that could consume the mouse events.

public class ComboBoxWithCellFactory extends Application {

    @Override
    public void start(Stage primaryStage) {
        ComboBox btn = new ComboBox();
        btn.setCellFactory(
                new Callback<ListView<String>, ListCell<String>>() {
                    @Override
                    public ListCell<String> call(ListView<String> param) {
                        final ListCell<String> cell = new ListCell<String>() {
                            {
                                super.setPrefWidth(100);
                            }

                            @Override
                            public void updateItem(String item, boolean empty) {
                                super.updateItem(item, empty);
                                if (item != null) {
                                    setText(item);
                                    Button btn = new Button("hola");
                                    btn.setOnAction(new EventHandler<ActionEvent>() {
                                        @Override
                                        public void handle(ActionEvent event) {
                                            throw new UnsupportedOperationException("Not supported yet.");
                                        }
                                    });
                                    btn.setOnMouseClicked(new EventHandler<MouseEvent>() {
                                        @Override
                                        public void handle(MouseEvent event) {
                                            throw new UnsupportedOperationException("Not supported yet.");
                                        }
                                    });
                                    setGraphic(btn);
                                } else {
                                    setText(null);
                                }
                            }
                        };
                        return cell;
                    }
                });
        
        btn.getItems().add("mundo");

        StackPane root = new StackPane();
        root.getChildren().add(btn);

        Scene scene = new Scene(root, 300, 250);

        primaryStage.setTitle("Hola mundo!");
        primaryStage.setScene(scene);
        primaryStage.show();
    }

    public static void main(String[] args) {
        launch(args);
    }

}