Broadband imaging systems that contain holographic lenses can be lightweight and have large apertures. We report a Fresnel diffraction analysis of an imaging system that consists of three lenses of arbitrary dispersion. A general solution is found for the wavelength dependence of the lenses to simultaneously correct the imaging system for both longitudinal and lateral paraxial chromatic aberration. As a special case, we describe an optical system that uses holographic lenses to produce a well-corrected image in broadband light. Experimental results that demonstrate the system performance in both laser and broadband illumination are reported.