Transfer functions with constant voltage sources in them?
The key is to remember that a voltage source generates whatever current is needed to assert the voltage difference. However, a DC voltage source (as drawn in your schematic) doesn't assert any AC voltage and therefore doesn't drive any AC current either.

So at any nonzero frequency, the voltage sources just look like shorts to ground. Kirchhoff's current law gets you the transfer function in this case.

At DC, consider the current \$I_1\$ through \$V_1\$ and \$I_2\$ through \$V_2\$. We must have \$I_i = I_1 + I_2\$, but also we must have \$\dfrac{I_1}{I_2} = \dfrac{R_2+R_3}{R_1}\$. Solving these for \$I_2\$, we get \$V_0 = V_2 + I_2 R_3\$.