I see references to this sort of split all the time, and not just from patients but also from highly educated physicians and scientists. Somehow they consider that our behavior* arises from two distinct sources: one composed of neurons, synapses, and neurotransmitters, and another composed of experiences, drives, and willpower.
If you buy the biological theory of behavior at all, then it makes little sense to imagine a dividing line between 'biological' and 'non-biological' causes of behavior. Experience alters neurochemistry just as surely as medications do.
Here's a nice (but somewhat technical) piece of work discussing some of the cellular-level changes that have been observed to be triggered by real-world experience (Takahashi, Svoboda and Malinow).
Evidence abounds for the utility of 'talk therapy' in psychiatry. In order to separate the 'biological' from the 'psychological,' one would have to believe that there exists an entirely separate underpinning of human behavior that operates on some ethereal plane, unrelated to the biomechanical world of synapses and neurotransmitters.
If you're going to accept that neurobiology underlies behavior, then there is no clear point at all where you can divide the biological from the psychological. If you accept that experience exerts its effects through alteration of our neuronal activity, and you accept that hearing your therapist is an experience, then there is no room for some nebulous 'non-biological' effect. Your therapist's words tickle your ear neurons, which tickle your brain neurons, which make subtle changes - sticking themselves to some of their neighbor cells, unsticking themselves from other neighbors, changing the rate at which they spit neurotransmitters at each other - and voila! You change your behavior.
That the line between biological and psychological is fuzzy to the point of nonexistence is indeed starting to permeate the general consciousness, at least to a degree. This usually arises in discussions of ethics, where the whole edifice of crime-and-punishment rests on an assumption of free will. This assumption is being radically challenged by evidence that our behavior is heavily determined by factors not under our direct control (genetics and medication in particular).
This opens up another can of worms, because we frequently associate 'biological' with 'beyond our control' and 'psychological' with 'within our control.' Hence my patient (and many like him) and his Magic Pill search.
But I think the educated world at large is not yet ready to join Steven Pinker in declaring us will-less playthings of our genes and environment. Fine for now, but I'm curious to see what we'll make of coming scientific advances that will no doubt push us even closer to the will-free wall.
*I'm using "behavior" intentionally to encompass all of the workings of the human brain that are manifest to others. I'm doing this very deliberately because the question of whether mind is biological at all is a very sticky wicket and not something I can afford to get into in this limited space.