In dual-channel supply chains, where retailers sell their goods both online and in physical stores, determining the optimal pricing strategy while considering customer behavior is a critical challenge. This study introduces and investigates a dual-channel pricing model that accounts for customer channel choice behavior. Drawing inspiration from market-share models, we incorporate a demand model that reflects the attraction between online and physical stores. Our approach includes stochastic assumptions for potential market demand and price-based interactions between the two channels. In particular, we model the channel’s stochastic demand as a non-linear function of prices and we allow for different customer reactions when the physical store runs out of stock. This paper makes two key contributions. First, we highlight the analytical complexity involved in verifying the joint concavity of the retailer’s expected profit function with respect to selling prices. To address this challenge, we introduce a novel approach to establish the existence of optimal global prices in the context of non-linear demand and a non-linear, non-concave objective function. Secondly, our study offers practical insights by applying the model to various operational scenarios. We provide guidance on the best pricing strategy when physical store capacity is limited. Depending on customer channel preferences, prioritizing the showroom may lead to higher profits. However, optimizing for profit could result in a reduced market share. In a showroom configuration, the retailer’s choice may shift between exclusive physical and exclusive online retailing to maximize profit.