  By virtue of the KP hierarchy reduction technique, we construct the general
bright-dark mixed $N$-soliton solution to the multi-component Mel'nikov system
comprised of multiple (say $M$) short-wave components and one long-wave
component with all possible combinations of nonlinearities including
all-positive, all-negative and mixed types. Firstly, the two-bright-one-dark
(2-b-1-d) and one-bright-two-dark (1-b-2-d) mixed $N$-soliton solutions in
short-wave components of the three-component Mel'nikov system are derived in
detail. Then we extend our analysis to the $M$-component Mel'nikov system to
obtain its general mixed $N$-soliton solution. The formula obtained unifies the
all-bright, all-dark and bright-dark mixed $N$-soliton solutions. For the
collision of two solitons, the asymptotic analysis shows that for a
$M$-component Mel'nikov system with $M \geq 3$, inelastic collision takes
place, resulting in energy exchange among the short-wave components supporting
bright solitons only if the bright solitons appear at least in two short-wave
components. Whereas, the dark solitons in the short-wave components and the
bright solitons in the long-wave component always undergo elastic collision
which just accompanied by a position shift.
