We propose a technique of multispectral incoherent holography. The differential wavefront curvature is measured, and the principle of Fourier transform spectrometry is applied to provide a set of spectral components of three-dimensional images and continuous spectra for spatially incoherent, polychromatic objects. This paper presents the mathematical formulation of the principle and the experimental results. Three-dimensional imaging properties are investigated based on an analytical impulse response function. The experimental and theoretical results agree well.