We construct a family of non-weight modules which are free $U\left(𝔥\right)$-modules of rank 2 over the $N=1$ super Schrödinger algebra in $(1+1)$-dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free $U\left(𝔥\right)$-modules of rank 2 over $\mathrm{𝔬𝔰𝔭}\left(1\right|2)$ are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.