makefiles: how to let it know where my headers are - makefile

Question

Assume I have the following file structure in my home directory
.
|-- foo
| `-- lib
| |-- bar.cpp
| `-- bar.h
|-- baz
| |-- qux.cpp
| `-- qux.h
|-- projects
| `-- src
| |-- makefile
` `-- main.cpp
and that main.cpp looks something like
#include "bar.h"
#include "qux.h"
// does stuff
What should my makefile look like?
Right now, it's something like the following
CC = g++
DEBUG = -g -Wall
STD = -std=c++11
OPTIMIZE = -O0
FOO_LIB = $$HOME/foo/lib
BAZ_LIB = $$HOME/baz
INCLUDES = -I$(FOO_LIB) -I$(BAZ_LIB)
LFLAGS = $(DEBUG) $(STD) $(OPTIMIZE) $(INCLUDES)
CFLAGS = -c $(LFLAGS)
BIN = $$HOME/my-program
OBJ = main.o \
bar.o \
qux.o
all: $(OBJ)
$(CC) $(LFLAGS) $(OBJ) -o $(BIN)
main.o: main.cpp bar.h qux.h
$(CC) $(CFLAGS) main.cpp bar.h qux.h
bar.o: bar.cpp bar.h
$(CC) $(CFLAGS) bar.cpp bar.h
qux.o: qux.cpp qux.h
$(CC) $(CFLAGS) qux.cpp qux.h
clean:
\rm *.o
\rm *.gch
But when I try that, I get
make: *** No rule to make target 'bar.h', needed by 'main.o'. Stop.
How do I let make know where my header files are? Even when I change
main.o to
main.o: main.cpp $(FOO_LIB)/bar.h $(BAZ_LIB)/qux.h
$(CC) $(CFLAGS) main.cpp $(FOO_LIB)/bar.h $(BAZ_LIB)/qux.h
it doesn't seem to work (at least with my more complicated real makefile).
Even if it did work, it seems like there's way too much mental overhead in
terms of making sure all of my dependencies are properly prefixed. (I took a
look at http://mad-scientist.net/make/autodep.html, but the sed stuff in
there is pretty impenetrable, and I'd like to sort of understand what I'm doing
so I can document it.)
#Etan Reisner
Let's assume my main.cpp #includes n headers in m library directories.
Does that mean my main.o recipe looks like this
main.o: main.cpp \
/path/to/foo1/bar1.h \
...
/path/to/foo1/barI.h \
...
/path/to/fooM/baz1.h \
...
/path/to/fooM/bazJ.h
$(CC) $(CFLAGS) main.cpp
If so, that looks like a lot of repetative work. Is there a straightforward
way of simplifying that?