  We consider elliptic transmission problems with complex coefficients across
an interface. Under proper transmission conditions, that extend known
conditions for well-posedness, and sub-ellipticity we derive microlocal and
local Carleman estimates near the interface. Carleman estimates are weighted a
priori estimates of the solutions of the elliptic transmission problem. The
weight is of exponential form, exp($tau$ {\phi}) where $tau$ can be taken as
large as desired. Such estimates have numerous applications in unique
continuation, inverse problems, and control theory. The proof relies on
microlocal factorizations of the symbols of the conjugated operators in
connection with the sign of the imaginary part of their roots. We further
consider weight functions where {\phi} = exp($\gamma$$\psi$), with $\gamma$
acting as a second large paremeter, and we derive estimates where the
dependency upon the two parameters, $tau$ and $\gamma$, is made explicit.
Applications to unique continuation properties are given.
