The scattering matrix approach is employed to determine a joint probability density function of reflection eigenvalues for chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Derived under assumption of broken time-reversal symmetry, this result is further utilised to (i) calculate the density and correlation functions of reflection eigenvalues, and (ii) study fluctuations properties of the Landauer conductance. In particular, in the limit of mode-independent tunneling, statistics of the conductance is shown to be governed by a two-dimensional Toda lattice equation.