Generally mirrors can be used for reflecting electromagnetic spectrum. A mirror can be broad band reflector or single wavelength reflector. Bragg mirrors made using multilayer thin films with alternating thickness and refractive index. By engineering the layer lattice, refractive index change and film thickness, one can also engineer the reflection or transmission band gap. Although some IR light is absorbed by metals, it can be totaly reflected using appropriate bragg reflectors. 

Links : http://www.batop.de/information/r_Bragg.html

http://en.wikipedia.org/wiki/Distributed_Bragg_reflector

My paper : http://scitation.aip.org/content/aip/journal/apl/105/7/10.1063/1.4893594

Here are a few possible advantages of all-dielectric vs metal mirrors:

• a higher reflectance in the reflectance band;
• a phase-change on reflection that is close to zero and varying linearly in the band of reflection (a metal can introduce a different phase-shift);
• in some cases, they can be more prone to aging and more resistance to high-power beams.

(1) Low loss, if the dielectric material is transparent to the wavelength under study. That means it can exhibit ultra-high reflectance, useful for high-Q cavity. One just needs to stack more pairs to produce more reflectance. In contrast, metal has a upper limit ~99.5%.

(2) Broadband. Yes, it can be as broad as metal, at a much higher reflectance.

(3) Predictable reflection phase. It is exactly pi or 0 at normal incidence of design wavelength, has weak dependence of reflection phase on incident angle and wavelength. Can be approximated as linear dependence in a small range, but not linear over broadband.

I don't know particularly why it is preferred in interferometer experiment setup. Above is all I can think of that are relevant facts about Bragg mirrors. For more details, you can read my paper, especially the supplementary material at the link below. 

Article Dispersion Engineering for Vertical Microcavities Using Subw...

Bragg mirrors are well suited for UV and EUV applications.