The altitude profile of electron density in the D region is determined using an array of GPS-phase-referenced VLF receivers, allowing for the simultaneous broadband (i.e., phase coherent) measurement of a 24.0 kHz signal at multiple sites ranging in propagation path length from 3060 to 3353 km. Measured data are compared with results of model calculations for four electron density profiles used in previous work, assuming a single density profile to be in effect along the entire signal path from transmitter to receiver. Interpolation between model profiles is used to find a new profile which best fits the data. Phase coherent measurements over a range of path lengths also allow for the identification of the parameters for individual waveguide modes. Measured mode parameters agree with model calculations, within the limitations imposed by the configuration of the present array. A methodology of analysis and the required set of measurements is described, which would allow the decomposition of a VLF signal into all of its constituent waveguide modes, and accurate measurement of the characteristic parameters of each mode, namely phase velocity, attenuation rate, amplitude, and phase.