  In this article, we study the notion of the Schur multiplier
$\mathcal{M}(N,L)$ of a pair $(N,L)$ of Lie superalgebras and obtain some upper
bounds concerning dimensions. Moreover, we characterize the pairs of finite
dimensional (nilpotent) Lie superalgebras for which $\dim \mathcal{M}(N,L)=
\frac{1}{2}\big{(}(m+n)^2+(n-m)\big{)}+\dim N\dim(L/N)-t$, for $t=0,1$, where
$\dim N=(m|n)$.
