Whether it's ethical or not is a moot question because in the US it would be illegal under federal law to do so unless the doctor has the patient's written permission to inform the others.
The law that prohibits this is known as the Health Insurance Portability and Accountability Act of 1996 (HIPAA). Specifically, the Privacy Rule of HIPAA identifies Protected Health Information (PHI) as follows:
Protected Health Information. The Privacy Rule protects all "individually identifiable health information" held or transmitted by
a covered entity or its business associate, in any form or media,
whether electronic, paper, or oral. The Privacy Rule calls this
information "protected health information (PHI)."
The specific restriction is as follows (same link, emphasis is mine):
Basic Principle. A major purpose of the Privacy Rule is to define and limit the circumstances in which an individual’s protected heath
information may be used or disclosed by covered entities. A covered
entity may not use or disclose protected health information, except
either: (1) as the Privacy Rule permits or requires; or (2) as the
individual who is the subject of the information (or the individual’s
personal representative) authorizes in writing.
Nowhere in the Privacy Rule does it permit informing family or cohabitants about infectious diseases -- or any PHI at all -- without the patient's permission.