  We analyze a simultaneous continuous measurement of photon-counting and
homodyne detection. The stochastic master equation or stochastic Schr\"odinger
equation describing the measurement process includes both jump-type and
diffusive-type stochastic increments. Analytic expressions of the wave function
conditioned on homodyne and photon-counting records are obtained, yielding the
probability density distributions and generating functions of the measurement
records. Formula for the expectation values of the homodyne records conditioned
on a photon-counting event is also derived which quantitatively describes the
measurement backaction of photon-counting on the homodyne output. The obtained
results are applied to typical initial states --- coherent, number, thermal,
and squeezed states. Monte Carlo simulations of the measurement processes are
also presented to demonstrate the dynamics of the combined measurement process.
