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We explore the multiwavelength radiation properties of the light curves and energy spectra in the dissipative magnetospheres of pulsars. The dissipative magnetospheres are simulated by the pseudo-spectral method with the combined force-free and Aristotelian electrodynamics, which can produce self-consistent accelerating electric fields mainly distributed in the equatorial current sheet outside the light cylinder. The multiwavelength light curves and spectra are computed by using the multiple emission mechanisms of both the primary particles accelerated by the accelerating electric fields in the equatorial current sheet and the secondary pairs with an assumed distribution spectrum. We then compare the predicted multiwavelength light curves and spectra with the observed data from the Crab, Vela, and Geminga pulsars. Our modeling results can systematically reproduce the observed trends of the multiwavelength light curves and the spectra for these three pulsars well.