Measurements of the thermal-expansion coefficient, the magnetostriction, and the specific heat of Zn-doped CuGeO3 single crystals (x less than or equal to 3.3%) in magnetic fields up to 16 T are presented. Measuring the lattice constant as a function of temperature, magnetic field, and doping concentration allows us to determine the concentration and field dependence of the averaged spin-Peierls order parameter. A strong reduction upon doping is observed and interpreted in terms of solitonlike defects of the dimerization. From these data the relationship between the averaged spin-Peierls order parameter in doped CuGeO3 and the transition temperature T-SP is extracted. The specific heat at low temperatures is dominated by doping induced low-energy excitations. The temperature and field dependence of the corresponding contribution to the specific heat is discussed in a model with random magnetic exchange constants. Studying the thermodynamic properties as a function of an external field, we determine the magnetic field vs temperature phase diagrams of Cu1-xZnxGeO3. Several systematic changes upon doping are revealed. In particular, we find a strong enhancement of disorder in doped CuGeO3, when entering the incommensurate phase with increasing field which we attribute to an additional randomness of the order-parameter phase. Moreover, this field-induced phase transition between dimerized and incommensurate phases is accompanied by a pronounced increase of the antiferromagnetic ordering temperature T-N. A phenomenological description assuming a coupling between the spin-Peierls and the antiferromagnetic order parameters is presented, which allows us to interpret simultaneously both field and concentration dependences of TN [S0163-1829(99)08305-8].