Microwave spectra of CH4- -H2O, CH4- -(H2O)-O-18, CH4- -(H2O)-O-17, CH4- -D2O, and CH4- -DOH have been measured using a pulsed-nozzle Fourier-transform microwave spectrometer. The spectra were recorded to aid the assignment of the high-resolution far-infrared spectrum of CH4- -H2O reported recently [L. Dore, R. C. Cohen, C. A, Schmuttenmaer, K. L. Busarow, M. J. Elrod, J. G. Leeser, and R. J. Saykally, J. Chem. Phys. 100, 863 (1994)]. Spectral assignments were guided by Stark-effect and nuclear-spin hyperfine measurements. For the primary isotopic species, CH4- -H2O, four K=0 (Sigma) and six K=1 (Pi) rotational progressions were observed at the similar to 1 K rotational temperature of the supersonic expansion. The internal-rotor state of the complex correlating to j=0 H2O+j=0 CH4 is found to have a rotational constant B=4346.7202(7) MHz and centrifugal distortion constant D-J=119.72(9) kHz, where the numbers in parentheses represent one standard deviation of the fit. These constants imply a zero-point center-of-mass separation of 3.7024 Angstrom between the two subunits and a pseudodiatomic weak-bond stretching force constant of 1.53 N/m and stretching frequency of 55 cm(-1). Stark-effect measurements reveal that two of the K=1 progressions originate from degenerate states while the other four K=1 transitions arise from two Pi states which are K (or l) doubled. The effective electric dipole moments vary from 1.95 X 10(-30) to 2.67 X 10(-30) C m (0.58-0.83 D) for the states studied. The isotopic results are consistent with a CH4- -H2O structure in which one of the hydrogens of H2O proton donates to CH4, analogous to structures previously reporteh for CH4 with HCN and HCl. A combined analysis of the microwave and far-infrared data allow estimates of the barriers to internal rotation of the H2O and CH4 units. The H2O internal rotation potential is found to be much more anisotropic than that of Ar- -H2O.