Transfer function of a cascaded passive + active filter
I would treat it like any other op-amp circuit.

Start at the right and work your way back.
(V_0-0)/R3=I0

That same current must flow from the - terminal to V1 so:
I0= (0-V1)/(R2+1/(sC2))

And the current going through R1 towards V1 is:
I1 = (Vi-V1)/R1

And the current flowing down from V1 is:
I2 = V1/(1/sC1)

Lastly, you know that the currents entering and leaving the nodes must be equal so at V1 you have:
I0+I1=I2

You should now have the equations to solve for everything in reference to Vo/Vi which is H(s)

Solving it all the way through I get this:
$$ H(s)=\frac{V_o}{V_i}=\frac{-R_3C_2S}{(R_1C_1S+1)(R_2C_2S+1)+R_1C_2S} $$

Hopefully I didn't muck that up in the algebra...

From the looks of it, it looks like a bandpass filter due to the single order S term in the top.