I'm basing this answer on long years of experience with the World Health Organization. I understand this to be a community outreach unit administered by a larger and more central health center. These posts/units are usually staffed by nurses and visited by a physician on regular schedule, whereas the health center will have at least one physician on duty full time.

'Community health unit' might be more appropriate for an urban area in a developed country.
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P-1056 Lisbon, Portugal;. Russian by the WHO Information Centre for ... and Community Health unit at the address given above. ...
www.euro.who.int/__data/assets/pdf_file/0015/74004/EN60.pdf

Health and health care in Portugal: does gender matter? By Céu Mateus, Julian Perelman and ... Family and Community Health unit at the address given above. ...
www.who.int/entity/reproductivehealth/topics/gender.../en66...

94, 2008/21985, BUSINESS DEVELOPMENT - Agreements - PORTUGAL - AGREEMENT POLICY .... FAMILY AND COMMUNITY HEALTH UNIT ( FCH ) PROJECT / 2008/02 PATHWAYS TO ...
www.facs.gov.au/about/.../1 JULY TO 31 DEC 2008.xls

.. Chaves M. Universidade Federal do Rio Grande do Sul Porto Alegre, Brasil. ... enrolled at a Community Health Unit in Porto Alegre, southern Brazil, ...
www.ncbi.nlm.nih.gov/pubmed/8734969

Goldstream Community Health Unit, Victoria, Canada - Hospital Listing
Address, contact information and map for Goldstream Community Health Unit.
www.hospitalsworldwide.com/listings/7318.php

Community Health Unit 440 3rd Street East Brooks, Alberta, T1R 1B3 T: 403-362-3388. F: 403-362-8126. Calgary. Medisys Travel Health Clinic ...
www.csih.org/en/travelhealth/alberta.asp


It is also used in developing countries:

Community Health Worker Training in Dertu, Kenya - Millennium ...
Sep 9, 2009 ... The Community Health Unit consists of about 1000 households or about 5000 ... Each community health unit should have a committee called a ...
blogs.millenniumpromise.org/.../community-health-worker-training-in-dertu/

Since 1995, the Community Health Unit of the Ministry of Health, Rwanda, has trained about 12000 community health workers who are living and working among ...
www.usaid.gov/rw/our_work/for.../nationalcommunityhealthpol...


'Community health post' is used in English when writing about Mozambique, for certain - maybe other Portuguese-speaking countries - but it might be considered too rural for the cities you mention.
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Community Health Post workers are mainly registered nurses. They ... community health post. Informally, the community health practitioners have been ...
www.springerlink.com/index/fv566273q0h03q42.pdf

Supporting a Local COMMUNITY HEALTH POST. GET INVOLVED and Help Make a ... I worked in the community health post, which involved assisting patients with ...
www.volunteeringnepal.org › Volunteer Programs

Oct 4, 2009 ... #2: The Health Department has requested our help in expanding the current Mucombezi Sede community Health Post (which the mission operates) ...
lynnlagore.blogspot.com/.../new-cool-neighbors-and-health-post-news.html

Sep 18, 2003 ... Three years ago the Tipitapa community health post looked much like ... The renewal of the community health post and the establishment of ...
www.ifrc.org/docs/news/03/03091801/