Starting with the semiclassical initial value representation (NR) for the description of a composite molecular system consisting of a "system" and a "bath," we show a systematic procedure whereby one can retain the semiclassical IVR description of the "system"-thus including quantum interference and tunneling effects for these degrees of freedom-while neglecting these effects in the "bath" degrees of freedom, thus reducing them to a classical description. The zeroth order version of this mixed semiclassical-classical model is seen to be the semiclassical equivalent of the Ehrenfest model (closely related to the TDSCF approximation), but higher order versions are also developed that go beyond this level. of approximation. Two levels of this theory are explicitly worked out. Numerical tests on simple but illustrative problems are used to discuss the merit of these approaches.