I've found that the average layperson, asked to describe physical chemistry or chemical physics, is unable to provide a definition. At best, he or she confuses physical with physiological and assumes an implicit connection to medical science. I can't blame them. There are too many subdivisions of chemistry for a person without a bachelor's degree in the sciences to keep them straight.
Chemistry by itself is the middle child of the sciences. It lacks the romantic associations of astronomy, the flamboyant geniuses of physics, the obvious utility of biology. In the public mind, it is practical and necessary, but it is also solved. Its most familiar representative, the periodic table, is complete, or at least, it lacks only elements with lifetimes on the scale of femtoseconds, which are hardly conducive to the construction of compounds we encounter in our daily lives. Chemists have done little to rectify this impression.
Scientific research that has technological relevance, that fires the imagination and that is successfully championed by a memorable personality will be viewed as valuable to society. The study of chemistry has much of the first, but little of the latter two. It acquires those qualities through its association with the other sciences, particularly biology. It could be argued that the push for interdisciplinary research over the past few years has affected biology, physics and astronomy, but I don't think it has become as pervasive as it has in chemistry. Witness, for instance, the recent appearance of the field known as "biophysical organic chemistry."
It seems as if chemists are no longer able to justify their research without looking to the other sciences. I'd like to see chemistry restored to a position of equality with the other scientific disciplines. I want to hear people who study atomic and molecular reactions; measure or model energetic, dynamic and kinetic properties of molecules; or synthesize new compounds for medical or industrial use call themselves chemists. There comes a point when attempting to improve the accuracy of the definition of a field of study does nothing but confuse and obfuscate. And, possibly more importantly, bore people to death. I'm not sure what can be done to improve chemistry's public image, but I'm pretty sure that the proliferation of prefixes has done much to dilute the perceived value of chemistry.