The Wertheim lattice thermodynamic perturbation theory is used to calculate the liquid-liquid and solid-liquid coexistence data of a model polymer solution. The theory predicts bimodal LCST phase behavior as well as an unusual step with composition in the solid-liquid equilibrium of the solvent. These theoretical predictions are discussed in relation to the experimental results obtained for the poly(vinyl methyl ether) (PVME)/D2O system. The apparent heat capacity signal from modulated temperature DSC (MTDSC) is used to measure the onset of LCST phase separation along with the melting temperature of D2O in the presence of PVME. The experimentally observed trace of the melting endotherm allows calculating the complete melting line of the solvent, in agreement with theory. Moreover, an alternative approach, employing Fourier transform infrared spectroscopy, is established from which the equilibrium melting line of D2O could be determined, again confirming theoretical predictions. The peculiar concentration dependence of the melting curve of ice provides a new explanation for W the double melting endotherm observed in (MT)DSC and (ii) the inhibited crystallization in highly concentrated aqueous PVME mixtures. Finally, the existence of a low-temperature UCST miscibility gap is suggested via an insightful examination of the glass transition region.