  In this paper, we construct approximations of the microscopic solution of a
nonlinear reaction--diffusion equation in a domain consisting of two
bulk-domains, which are separated by a thin layer with a periodic heterogeneous
structure. The size of the heterogeneities and thickness of the layer are of
order $\epsilon$, where the parameter $\epsilon$ is small compared to the
length scale of the whole domain. In the limit $\epsilon \to 0$, when the thin
layer reduces to an interface $\Sigma$ separating two bulk domains, a
macroscopic model with effective interface conditions across $\Sigma$ is
obtained. Our approximations are obtained by adding corrector terms to the
macroscopic solution, which take into account the oscillations in the thin
layer and the coupling conditions between the layer and the bulk domains. To
validate these approximations, we prove error estimates with respect to
$\epsilon$. Our approximations are constructed in two steps leading to error
estimates of order $\epsilon^{\frac12}$ and $\epsilon$ in the $H^1$-norm.
