Maximum Voiced Frequency (MVF) is used in various speech models as the spectral boundary separating periodic and aperiodic components during the production of voiced sounds. Recent studies have shown that its proper estimation and modeling enhance the quality of statistical parametric speech synthesizers. Contrastingly, these same methods of MVF estimation have been reported to degrade the performance of singing voice synthesizers. This paper proposes a new approach for MVF estimation which exploits both amplitude and phase spectra. It is shown that phase conveys relevant information about the harmonicity of the voice signal, and that it can be jointly used with features derived from the amplitude spectrum. This information is further integrated into a maximum likelihood criterion which provides a decision about the MVF estimate. The proposed technique is compared to two state-of-the-art methods, and shows a superior performance in both objective and subjective evaluations. Perceptual tests indicate a drastic improvement in high-pitched voices.