In this paper, we present a comprehensive stochastic model describing the measurement uncertainty, output signal, and limits of detection of affinity-based biosensors. The biochemical events within the biosensor platform are modeled by a Markov stochastic process, describing both the probabilistic mass transfer and the interactions of analytes with the capturing probes. To generalize this model and incorporate the detection process, we add noisy signal transduction and amplification stages to the Markov model. Using this approach, we are able to evaluate not only the output signal and the statistics of its fluctuation but also the noise contributions of each stage within the biosensor platform. Furthermore, we apply our formulations to define the signal-to-noise ratio, noise figure, and detection dynamic range of affinity-based biosensors. Motivated by the platforms encountered in practice, we construct the noise model of a number of widely used systems. The results of this study show that our formulations predict the behavioral characteristics of affinity-based biosensors which indicate the validity of the model.