I have fixed the issue with the UI being half-network-wide and half-site-specific (i.e. using the judaism images but the stackexchange background).
However! Your question is based on a false premise: as far as the system is concerned, the host for judaism is judaism.stackexchange.com; you might refer to it as mi.yodeya, but that does not make it the host. Chat is entirely correct to link to judaism.stackexchange.com, and not mi.yodeya.com (which exists only as a redirect).
Balpha is also correct to say that if you invent your own urls (based on nothing that the system has given you), then it is not unreasonable to expect odd results; however, the "half this and half that" offended my sense of correctness, even for an invalid URL.
If and when your other request comes to pass, then we would re-point those rooms. Until then: chat is correct.