The maximum measurable range of a spectral interference microscope depends on the coherence length of the light transmitted by its tunable spectral filter. To achieve a large range in step-height measurement we have developed a new tunable spectral filter that uses tandem liquid-crystal Fabry-Perot interferometers (LC-FPIs), which can simultaneously attain both a high spectral resolution and a large tuning range. Fringe visibility measurements were carried out, and it was found that the coherence length of the light transmitted through tandem LC-FPIs is two times larger than that transmitted through a single LC-FPI. Using this novel tunable spectral filter, we developed a new spectral interference microscope for the measurement of three-dimensional shapes of discontinuous objects. Experimental results of step-height measurements both with a single LC-FPI and with tandem LC-FPIs are presented for a combination of standard steel gauge block sets with 1-, 99-, and 100-microm steps. A large range (1-100 microm) of measurement with submicrometer resolution was achieved with tandem LC-FPIs that was not possible with our previous system in which a single LC-FPI was used.