Assume that there exist banks which accept deposits during the initial capital market, then allow customers to withdraw their deposits if they turn out to have H equal to 1. Deposits earn competitive interest if not withdrawn. Consumers learn their type. They withdraw their funds if necessary. Consumers receive income from sale of their endowment, receive bonds and deposits, and pay or receive whatever tax or transfer is needed.
Consumers purchase second period consumption.
They receive income from sales of endowment, and repay their money to the government. In this setting, the real interest rate is determined independent of the money supply. Each individual gets to spend the present value of his endowment in the appropriate period. Then the behavior of consumers and banks is straightforward. And from here on, the model will work in pretty much the same way as the pure outside money model in the text.