This paper presents a theoretical framework for analyzing pricing structures in debit card schemes featuring cardholders, retailers, their respective banks, and a network routing switch. The network routing switch controls the electronic debit card network and is jointly owned by the banks. In setting its prices, it needs to consider getting both consumers and retailers to participate in the market. In this two-sided market for debit cards, we show that the "double-monopolistic" network routing switch may want to supply consumers with cheap debit cards, deriving profits from charging a high retailer fee per transaction. This theoretic result resembles the current practice in the Netherlands where consumers pay no transaction fee, but retailers do. This corner solution carries over when we analyze socially optimal pricing.