|Abstract||Joint measurements of multiple qubits open new possibilities for quantum information processing. Here we present an approach based on homodyne detection to realize such measurements in the dispersive regime of cavity or circuit QED. By changing details of the measurement, the readout can be tuned from extracting only single-qubit to extracting only multiqubit properties. We obtain a reduced stochastic master equation describing this measurement and its effect on the qubits. As an example, we present results showing parity measurements of two qubits. In this situation, measurement of an initially unentangled state can yield, with near unit probability, a state of significant concurrence.