Pseudo-2-dimensional models are routinely used to predict the lithiation curves for energy storage devices, including lithium-metal batteries. The performance of such models is as good as their parameterization, which remains a challenge especially in the presence of \textcolor{blue}{carbon binder domain} (CBD). We propose two alternative parameterization strategies, which explicitly account for the CBD volume fraction and physical properties. The first aggregates CBD with the electrolyte-filled pore space and expresses the Bruggeman exponent in terms of a solution of microstructure-specific closure problem. The second treats CBD and active particles as a composite solid phase, whose effective properties are computed (semi-)analytically via homogenization. We show that the latter strategy used to parameterize the Doyle-Fuller-Newman model provides an attractive middle ground between the model complexity and the prediction accuracy. Our modeling results suggest that the battery discharge time decreases as either the CBD volume fraction increases or the CBD ionic diffusivity decreases, and is insensitive to the CBD ionic conductivity. The quantitative nature of these observations can be used in the optimal design of porous cathodes.