Interpretation of a PhD degree in a very broad, interdisciplinary field Back when my older brother started his PhD degree I asked him what it meant to be a doctor in something other than medicine. I don't recall the exact wording he used, but the idea he portrayed was that you take a field, a narrow and specific field, and you specialise in it to a level at which when you are done, you have become one of the ultimate experts in that very specific field. 

For instance if you are working with combustion physics, you might be one of the leading experts in efficient 2 cylinder, ultra-light engines made out of refined aluminium... Alternatively if you are into neuroscience you might be an expert on a particular neurotransmitter re-absorption in a particular zone of the brain following heavy exercise (or whatever, hopefully you get the point). It might be an opinionated view of a PhD but I feel it's a common way to look at a PhD degree; a certification of expertise. 

Fast-forward 15 years... I am about half-way in my PhD studies in the highly interdisciplinary field of bioinformatics, where statistics, mathematical modeling, physics, molecular chemistry and programming boil together with cell biology, to top it all you typically have a theme spice, which in my case is cancer biology. I have a growing feeling that I am getting stretched thinner and thinner by the day, instead of becoming increasingly competent in a specific field, I become semi-competent in increasingly many fields. 

That being the case I am not sure I (or others like myself) will fit the "definition" above. I would appreciate some perspective as to how one should be seeing highly interdisciplinary PhD studies and the development (as a scientist and a professional) that graduate studies entitles. Subsequently, how should one go about to profile him/her-self to future employers, seeing as there is no one natural field to pursue, but rather many different ones.
I completely understand your feeling. I can tell you that many other people in this field feel the same. This has nothing to do with how smart or how good they are. This issue also bugged me a lot, but I can offer some insights:


Bioinformatics/computational biology is really huge and you cannot be an expert in all aspects. Even if you look at senior scientists in this field, I do not think there is someone who is an expert in all subfields. You simply can't master all the physics, math, CS, chemistry and biology at an expert level - even in a much longer time than a PhD.
You can still have a huge impact without being a super-expert in every subfield. Just look at some of the research published in top journals. The reason is that you will have knowledge and a way of thinking that people restricted to a single field may not have. From personal experience, I can say that this is a significant advantage for asking certain types of questions and coming up with certain ideas that single-field specialists won't come up with.
After a while you will realize that you actually are an expert. Maybe not in the sense that you know everything about everything, but you will see that you can give good advice to other people, foresee potential problems, and so on. In addition to knowing a lot about computational biology, you will become an expert in things such as quantitative modelling, applied machine learning and "big data" analysis (I hate that term), skills which are very useful in a wide range of fields.
The fact that you cannot become an expert in everything doesn't mean you should neglect learning. On the contrary, you should constantly try to expand your knowledge in all related fields. And yes, it can be more difficult than learning only one subject.
Finally, in the end you will be working on a specific problem in a given biological problem with a given set of tools. That problem is what you really need to be an expert on.