[en] The strong power law behavior of the specific heat jump $\mathrm{\Delta <!--\; ??\; -->}C$ versus T _c $(\mathrm{\Delta <!--\; ??\; -->}C/T_{\mathrm{c}}\sim <!--\; ???\; -->T_{\mathrm{c}}^{\mathrm{\alpha <!--\; ??\; -->}},\mathrm{\alpha <!--\; ??\; -->}\approx <!--\; ???\; -->2)$, first observed by Bud’ko et al (2009 Phys. Rev. B 79 220516), has been confirmed with several families of the Fe-based superconducting compounds with various dopings. We have tested a minimal two band BCS model to understand this anomalous behavior and showed that this non-BCS relation between $\mathrm{\Delta <!--\; ??\; -->}C$ versus T _c is a generic property of the multiband superconducting state paired by a dominant interband interaction ($V_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}}><!--\; >\; -->V_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}}$) reflecting the relation $\frac{{\mathrm{\Delta <!--\; ??\; -->}}_{\mathrm{h}}}{{\mathrm{\Delta <!--\; ??\; -->}}_{\mathrm{e}}}\sim <!--\; ???\; -->\sqrt{\frac{N_{\mathrm{e}}}{N_{\mathrm{h}}}}$ near T _c, as in the $S_{\pm <!--\; ??\; -->}$-wave pairing state. We also found that this $\mathrm{\Delta <!--\; ??\; -->}C$ versus T _c power law can continuously change from the ideal BNC scaling to a considerable deviation by a moderate variation of the impurity scattering rate ${\mathrm{\Gamma <!--\; ??\; -->}}_0$ (non-pair-breaking). As a result, our model provides a consistent explanation why the electron-doped Fe-based superconductors follow the ideal BNC scaling very well while the hole-doped systems often show varying degree of deviations. (paper)