  We introduce a semisimple tensor category $\mc{O}^{int}_q(m|n)$ of modules
over an quantum ortho-symplectic superalgebra. It is a natural counterpart of
the category of finitely dominated integrable modules over the quantum
classical (super) algebra of type $B_{m+n}$, $C_{m+n}$, $D_{m+n}$ or $B(0,m+n)$
from a viewpoint of super duality. We classify the irreducible modules in
$\mc{O}^{int}_q(m|n)$ and show that an irreducible module in
$\mc{O}^{int}_q(m|n)$ has a unique crystal base in case of type $B$ and $C$. An
explicit description of the crystal graph is given in terms of a new
combinatorial object called ortho-symplectic tableaux.
