I did 1 year of research my last year of undergrad, I've worked in a community mental health clinic and also in an academic research lab. I wouldn't call myself bilingual (no one's going to confuse me with a native speaker), but I have worked in a "bilingual" position. I've worked with adults, adolescents, and children with psychopathologies and substance abuse issues.
One of the only major issues I can think of is that my area of interest within health psychology is an emerging area and at this point most of the experts in the field work only with adults. Much of the work in this area with kids seems to be the result of one of the experts who works with adults collaborating with another faculty member who works with kids and adolescents. I've been asked about whether I'd be happy not working with kids. My answers and my personal statement convey pretty clearly that learning the intervention/methods in my specific area of interest is primary, although I want my training to be well-rounded enough that I can adapt it to multiple age groups and family interventions. For me this means that my research and dissertation may only be with adults but my practica involve rotations in family and C&A services. It could also mean doing an internship in pediatric psychology or a post-doc in it so I have the qualifications to work with all members and ages in a family or family dyads.
Well, first, it does sound like you did get some interviews, so congratulations on those! There is a certain amount of luck in the system, and people just don't get every interview they'd like. Unlike law school, for example, where if your GPA and LSAT score are high enough, you're likely to make the cut. And that's definitely tough for overachievers like many of us who are used to trying hard and believe the saying "if you work hard enough, you can get it."
That said, as I'm now on the other side of the admissions process, I can think of a couple of things that may not have been ideal. I'm not sure how long you've been out, but you say a year of research experience. Are you applying straight out of undergrad or have you been out doing research a couple of years? I'd say people who are coming straight out are at a disadvantage, in general. If you have been out longer, have you been doing research in that time? A year just isn't that much research experience.
Second, it sounds like you're a pediatric health psych person, who applied to work with a lot of adult health psych people (potentially because of health psych tracks). I know there are fewer peds health people out there, and that can be an issue, and it's unfortunate. But, for the places where you said you wanted to do peds health, child placements, but wanted an adult health mentor, I think that's a tough sell. I know what you mean and how you could combine strengths, but depending on the program, that's more or less feasible. My program has somewhat of a child track and health track, and although it's all part of one program, the faculty on those tracks are pretty disparate. All the people working with health faculty are adult people, do adult research, and are linked into those adult health placements. Similarly, the child people do child research, child placements, AND the peds placements, even if they're not directly doing peds research. I would think that if someone wrote they wanted to work with Dr. X health and Dr. Y child on their statement, it just would look odd. Dr. X would feel they couldn't guide you in child stuff, and Dr. Y would feel that they weren't really a research match, so both would worry about fit if they were your primary mentor. Plus, especially to casual readers of your statement, it would look like you didn't really know what you wanted since your mentor interests were so different, and people just don't apply to work with that combo of people. Most people's statements read Dr. A child, Dr. B child, and Dr. C child in terms of mentor interests, where you can more easily see the connection because those people's research are somewhat related.
That said, I know what you mean, and I know there are peds programs out there, or child researchers who have a health component, even if its not their major focus. Plus, focus on the interviews you have!! You've gotten some, and better to focus on those and on the future than contemplate what happened to the ones that didn't.