Governance and government are interchangeable in the sense the process of governing, but they differ in other senses. Government often refers to the governing body itself, while governance often refers to the act of governing. So members of a government are engaged in governance.
Meanwhile, governance is often the better word for the administration of nongovernmental organizations (corporations, for example), while government works better in reference to the public administration of nations, states, municipalities, etc.
Examples
Governance works in the following sentences, but government could replace it:
For all the talk of bipartisan governance, Brown has appointed only 10 registered Republicans to vacant positions. [San Francisco Chronicle]
By 2005, every state but Madagascar had established a democratic system of governance. [The Dominion Post]
Governance usually works better for nongovernment organizational administration—for example:
It falls to the trustees to ensure their organisation gets its governance right. [Guardian]
A review of Australian cricket governance says the states do not trust the Cricket Australia board. [Australian]
It argued that ENRC’s corporate governance was no worse than Russian peers and could only improve. [Financial Times]
And though government can mean the act or process of governing, governance is favored for this purpose—for example:
[S]ome of his followers suggested he believed the route to good governance lay in the knowledge and professional competence of the few rather than in the opinions of the many. [CBC]
They echo the many problems of modern governance in China, and show how shallow the reservoir of political support for elites can often be. [Wall Street Journal]