Facial imaging and facial recognition technologies, now common in our daily lives, also are increasingly incorporated into health care processes, enabling touch-free appointment check-in, matching patients accurately, and assisting with the diagnosis of certain medical conditions. The use, sharing, and storage of facial data is expected to expand in coming years, yet little is documented about the perspectives of patients and participants regarding these uses. We developed a pair of surveys to gather public perspectives on uses of facial images and facial recognition technologies in healthcare and in health-related research in the United States. We used Qualtrics Panels to collect responses from general public respondents using two complementary and overlapping survey instruments; one focused on six types of biometrics (including facial images and DNA) and their uses in a wide range of societal contexts (including healthcare and research) and the other focused on facial imaging, facial recognition technology, and related data practices in health and research contexts specifically. We collected responses from a diverse group of 4,048 adults in the United States (2,038 and 2,010, from each survey respectively). A majority of respondents (55.5%) indicated they were equally worried about the privacy of medical records, DNA, and facial images collected for precision health research. A vignette was used to gauge willingness to participate in a hypothetical precision health study, with respondents split as willing to (39.6%), unwilling to (30.1%), and unsure about (30.3%) participating. Nearly one-quarter of respondents (24.8%) reported they would prefer to opt out of the DNA component of a study, and 22.0% reported they would prefer to opt out of both the DNA and facial imaging component of the study. Few indicated willingness to pay a fee to opt-out of the collection of their research data. Finally, respondents were offered options for ideal governance design of their data, as "open science"; "gated science"; and "closed science." No option elicited a majority response. Our findings indicate that while a majority of research participants might be comfortable with facial images and facial recognition technologies in healthcare and health-related research, a significant fraction expressed concern for the privacy of their own face-based data, similar to the privacy concerns of DNA data and medical records. A nuanced approach to uses of face-based data in healthcare and health-related research is needed, taking into consideration storage protection plans and the contexts of use.