There is no such thing as a "DC sine wave." I suspect you mean what would more
correctly be described as a 10 volt peak- to-peak sine wave with a +10 volt DC offset.

Not that it's that important, but I don't see why a "DC sine wave" is
an impossible concept, considering the definition of DC as a current
which flows in one direction:

http://www.answers.com/topic/direct-current

A "DC Sine wave" doesn't say that current reverses direction, only that
the current flow wanes and waxes.....like a river is still a river even
though its flow varies with rainfall...

The principle of superposition applies: the currents and voltages in the circuit will be
the sum of those that would result if the DC voltage and the AC sine wave were applied
to it seperately.

O.K. - now we're getting somewhere......you're saying the current and
voltage (and the implied impedance Z = V/I) of the "DC sine wave" is
the sum of the respective current and voltage of a +10V DC signal and a
-5V/+5V AC signal going into the same load.

Example:
DC +10V into load produces 1 Amp, therefore implied resistance = 10
ohm.
and
AC -5V/+5V (and given frequency) into load produces 0.5 amps, therefore
implied impedance = 20 ohms,

then what would the superposition prinicple predict as the resulting
combined current and impednace?