When you need to know how distance-hereditary graphs, chordal bipartite graphs, cographs, and bipartite distance-hereditary graphs are related (as I did while preparing slides for my GD05 talk), the Information System on Graph Class Inclusions and its big list of graph classes are the perfect resources.

FYI: cographs are a subclass of distance-hereditary graphs, as are the bipartite distance-hereditary graphs. Bipartite distance-hereditary graphs are also a subclass of the chordal bipartite graphs. Chordal bipartite graphs are a subclass of the bipartite graphs, but are not a subclass of the chordal graphs. Now you know why you need a web site to keep them straight.