There is a big debate in monetary theory whether the balance sheets of central bank and government should be shown as one or not. One side argues that the central bank is a government agency, and hence it would not make sense to create a balance sheet for both the central bank and government. Instead, they should be consolidated (see slides by Eric Tymoigne). Given what McAdoo says and what the NY Fed recently wrote about direct purchases of treasuries by the Fed I am quite convinced that consolidation is a sound approach, even though for pedagogical reasons it might still make more sense to show two balance sheets rather than on when it comes to government and its fiscal agent: the central bank. Here is an excerpt of the abstract from that NY Fed paper by Kenneth Garbade:
Until 1935, Federal Reserve Banks from time to time purchased short-term securities directly from the United States Treasury to facilitate Treasury cash management operations. The authority to undertake such purchases provided a robust safety net that ensured Treasury could meet its obligations even in the event of an unforeseen depletion of its cash balances. Congress prohibited direct purchases in 1935, but subsequently provided a limited wartime exemption in 1942.