We determine the joint probability density function (JPDF) of reflection eigenvalues in three Dyson's ensembles of chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Expressing the JPDF in terms of hypergeometric functions of matrix arguments (labeled by the Dyson index β), we further relate it to the β-Selberg correlation integral and prove that reflection eigenvalues form a determinantal ensemble at β=2 and a new type of a Pfaffian ensemble at β=4. As an application, we derive a simple analytic expression for the concurrence distribution describing production of orbitally entangled electrons in chaotic cavities with tunnel contacts when time reversal symmetry is preserved.