I can see why you might prefer an MPH, and think your commitment to combining public health with technical knowledge in informatics is a great idea (as well as being a very "hot" field right now). How easy or difficult it is to pursue a focus in bioinformatics while doing an MPH (probably in Biostatistics or Quantitative Methods or a related track) will almost certainly depend on the school's course and capstone requirements and the diversity of course offerings.
One more question I should have asked: What aspects of Health Informatics appeal to you? Different people (and different schools) would define it differently. A web page for Emory's PhD program says the following: "Bioinformatics is a term that means many different things to different people. From the statistical point of view, it encompasses dealing with gene and protein sequence data, large data sets, microarray data, multiple comparisons, brain imaging data, other imaging applications, interfacing statistics with computer science and theory of databases, data mining, geographical information systems, and statistical genetics. Bioinformatics is becoming increasingly widespread, including in association with the fields of biostatistics and statistics." I think many other schools have a narrower idea of what bioinformatics includes (e.g. limited to algorithms and applications for data mining, gene sequence comparison, protein structure prediction, etc., at a molecular level), though they may also have programs that would allow you to, for example, use GIS as a tool for epidemiology, or do genetic epidemiology (which may be specialized programs, or which may exist within epidemiology departments, for example). At some institutions, "health informatics" also encompasses things like computer systems for managing patient data. What in particular does "Health Informatics" mean to you, and how do you see yourself using it? This could help determine which programs will actually teach you what you need to know and give you a degree you can use.
P.S. There are more programs out there than I realized. Google is a great source of information! You might want to use it to search for programs that fit your preferred geographic and other parameters.
Emory *does* have both a MSPH and a newer certificate program in Public Health Informatics, either of which might fit your needs - see
http://www.sph.emory.edu/bios/phi.php and
http://www.sph.emory.edu/bios/phicertificate.php for more information.
University of Illinois - Chicago (UIC) has an online MPH in PHI:
http://www.uic.edu/sph/phi/
University of Alabama - Birmingham has a MSHI, geared more towards design and administration of health data tracking systems:
http://main.uab.edu/Shrp/default.aspx?pid=77369
