The application of microarray hybridization theory to Affymetrix GeneChip data has been a recent focus for data analysts. It has been shown that the hyperbolic Langmuir isotherm captures the shape of the signal response to concentration of Affymetrix GeneChips. We demonstrate that existing linear fit methods for extracting gene expression measures are not well adapted for the effect of saturation resulting from surface adsorption processes. In contrast to the most popular methods, we fit background and concentration parameters within a single global fitting routine instead of estimating the background before obtaining gene expression measures. We describe a non-linear multi-chip model of the perfect match signal that effectively allows for the separation of specific and non-specific components of the microarray signal and avoids saturation bias in the high-intensity range. Multimodel inference, incorporated within the fitting routine, allows a quantitative selection of the model that best describes the observed data. The performance of this method is evaluated on publicly available datasets, and comparisons to popular algorithms are presented.