Massive (≳8 M☉) stars may end their lives in the molecular clouds in which they were born. O-type stars probably have sufficient photoionizing radiation and wind power to clear a region more than 15 pc in radius of molecular material. Early B stars (B1-B3 on the main sequence, or 8-12 M☉ stars) are not capable of this and may interact directly with molecular gas when they explode. Molecular clouds are known to be clumpy, with dense molecular clumps occupying only a few percent of the volume. A supernova remnant then evolves primarily in the interclump medium, which has a density nH=5-25 H atoms.cm–3. The remnant becomes radiative at a radius of ∼6 pc, forming a shell that is magnetically supported. The structure of the shell can be described by a self-similar solution. When this shell interacts with the dense clumps, the molecular shock fronts are driven by a considerable overpressure compared to the pressure in the rest of the remnant. The expected range of clump sizes leads to a complex velocity distribution, with the possibility of molecular gas accelerated to a high velocity. Observations of the remnants W44 and IC 443 can be understood in this model. W44 has a shell expanding at ∼150 km.s–1 into a medium with density 4-5 cm–3. The shock emission expected in such a model is consistent with the observed Hα surface brightness and the [O I] 63 µm line luminosity. The clump interaction is seen in OH maser emission, which shows a magnetic field strength that is consistent with that expected in the model. IC 443 appears to be expanding at a lower velocity, 100 km.s–1, into an interclump medium with a higher density, ∼15 cm–3. The interaction of the radiative shell with molecular clumps can produce the molecular emission that is observed from IC 443. Both remnants are shell sources of radio synchrotron emission, which can be attributed to relativistic electrons in the cool radiative shell. If ambient cosmic-ray electrons are further accelerated by the shock front and by the postshock compression, the radio fluxes and the flat spectral indices of W44 and IC 443 can be explained. The energetic electrons are in a high-density shell and their bremsstrahlung emission can approximately produce the γ-ray fluxes observed by EGRET. Molecular clouds have a significant uniform magnetic field component so that heat conduction is likely to be important in the hot interior and can explain the isothermal X-ray emission observed from the remnants.