The complex Finsler space $E'$ is formed in such a way, that its tangent space $T(E')$ is equal to $T(F_1)\otimes iT(F2)$, where $F_1$ and $F_2$ are two $2n$-dimensional Finsler spaces. Using the nonlinear connections $N$ and $\bar N$ of $F_1$ and $F_2$ respectively, the adapted basis $B'$ of $T(E')$ is formed. There is given the complete list of $F(2)$ type, structures. Some of them for different values of parameters are almost complex, almost product or tangent structures.