The current paper estimates the overall inefficiency indicator of a bank under a network Data Envelopment Analysis (DEA) in the presence of undesirable inputs and outputs. We primarily contribute to the DEA literature in four ways. First, we decompose banks’ overall inefficiency performance indicator into five component indicators, namely, the sub-indicators of innovation, two kinds of stability, profitability and corporate social responsibility. Second, since the proposed model, which is an absolute value optimization problem, does not give the overall inefficiency score directly, we introduce a two-step procedure to obtain all sub-indicator scores and the overall inefficiency score. Third, we extend the by-production framework by proposing not only a concept and interpretation of “strategic disposability” for an intermediate undesirable output in estimating the stability sub-indicators, but also another concept of “strategic disposability” for an intermediate undesirable input in gauging the sub-indicator related to corporate social responsibility. Our results show that 1) the Chinese banking industry has a high level of innovation inefficiency and profitability inefficiency is higher than primary business stability inefficiency, strategic management stability inefficiency and corporate social responsibility inefficiency for all the bank ownership types except the state-owned commercial banks; 2) state-owned commercial banks have a higher level of corporate social responsibility inefficiency compared to the other inefficiencies; 3) state-owned commercial banks, rural commercial banks and joint-stock commercial banks are the best three performers with different ownership types performing well in different perspectives; 4) all different ownership types experience a level of performance volatility over the examined period.