Statistical parametric synthesizers usually rely on a simplified model of speech production where a minimum-phase filter is driven by a zero or random phase excitation signal. However, this procedure does not take into account the natural mixed-phase characteristics of the speech signal. This paper addresses this issue by proposing the use of the complex cepstrum for modeling phase information in statistical parametric speech synthesizers. Here a frame-based complex cepstrum is calculated through the interpolation of pitch-synchronous magnitude and unwrapped phase spectra. The noncausal part of the frame-based complex cepstrum is then modeled as phase features in the statistical parametric synthesizer. At synthesis time, the generated phase parameters are used to derive coefficients of a glottal filter. Experimental results show that the proposed approach effectively embeds phase information in the synthetic speech, resulting in close-to-natural waveforms and better speech quality.