I don't think Henry is in love just yet, but he is keenly interested in getting to know Catherine much better. As far as jealousy for JT is concerned, that's hard to say. Part of me sees Henry probing for CM's opinion of the buffoon before them, (i.e. how will this perfectly sweet girl describe something distasteful), while another part of me sees Henry trying to change the subject and remove JT from Catherine's mind, (providing her with a more enjoyable subject, like himself.)