How are Christianity and Judaism interrelated?

In one respect, Christianity and (OT) Judaism are asymmetrically related. The OT must validate Christianity. And (OT) Judaism developed independently of Christianity.

In another respect, if Christianity is true, then God inspired the OT and orchestrated OT history with a view to the NT and Christianity. In that regard they are teleologically interdependent.

Finally, that has reference to pre-Christian Judaism, but post-Christian Judaism (e.g. rabbinic Judaism) was reformulated in reaction to Christianity. Take Alan Segal's findings about how pre-Christian Judaism was open to a second Yahweh paradigm. At the time, that was within the bounds of normative Judaism. That only became heretical or intolerable after the rise of Christianity. In that respect, the asymmetry is in reverse: rabbinic Judaism is to some degree conceptually dependent on Christianity–by using Christianity as a foil and redefining Jewish monotheism to exclude what was permissible prior to the confrontation with Christianity. 

In that regard, rabbinic Judaism is analogous to the relation between pre-Reformation and Counter-Reformation Catholicism, where pre-Reformation Catholicism was more diverse.