We present the first simultaneous multi-line fitting of a semi-empirical atmospheric model with a chromosphere and transition region to the H\,{\sc I} and Ca\,{\sc II} spectra of an RS CVn star (II Peg). The static component of the H$\alpha$ emission core, the line profile of H$\beta$, the apparent absence of H$\gamma$ and H$\delta$, and the emission core profiles of Ca\,{\sc II} $K$ and two of the Ca\,{\sc II} $IR^3$ lines are all approximately fitted by a static $1D$ model with the following properties: $\log m$ at the onset of the transition region is $\approx -2.85$, and a $6000$ K plateau in the upper chromosphere that spans about a decade in $\log m$. In particular, the model is able to reproduce the unusually steep Balmer decrement (compared to the dMe stars), in which H$\alpha$ is strongly in emission and H$\beta$ is in absorption, without recourse to extra-atmospheric material. The Ca\,{\sc II} $IR^3$ lines are best fit by a model in which $T_{\rm min}$ is cooler by $300$ K and shallower by over half a decade in $\log m$ than that which best fits the optical lines. The emergent flux in the $IR^3$ line cores arises from the $T_{\rm min}$ region, whereas the other diagnostics arise from layers well above $T_{\rm min}$, and it is postulated that this may be the cause of the discrepancy. There has very recently been evidence from other investigators that the metallicity of II Peg may be sub-solar, and we find that models with $[{A\over H}]=-0.4$ provide a somewhat better fit to all the lines considered.