By means of scanning tunneling microscopy/spectroscopy (STM/STS), photoelectron spectroscopy, and first-principles calculations, we have studied the bismuth (Bi) adsorbate-stabilized InSb(100) substrate surface which shows a c(2X6) low-energy electron diffraction pattern [thus labeled Bi/InSb(100)c(2X6) surface] and which includes areas with metallic STS curves as well as areas with semiconducting STS curves. The first-principles phase diagram of the Bi/InSb(100) surface demonstrates the presence of the Bi-stabilized metallic c(2X6) reconstruction and semiconducting (4X3) reconstruction depending on the chemical potentials, in good agreement with STS results. The existence of the metallic c(2X6) phase, which does not obey the electron counting model, is attributed to the partial prohibition of the relaxation in the direction perpendicular to dimer rows in the competing reconstructions and the peculiar stability of the Bi-stabilized dimer rows. Based on (i) first-principles phase diagram, (ii) STS results, and (iii) comparison of the measured and calculated STM and photoemission data, we show that the measured Bi/InSb(100)c(2X6) surface includes metallic areas with the stable c(2X6) atomic structure and semiconducting areas with the stable (4X3) atomic structure.