We use both photometric and spectroscopic data from the {it Hubble Space Telescope} to explore the relationships among 4000 AA break (D4000) strength, colors, stellar masses, and morphology, in a sample of 352 galaxies with log$(M_{*}/M_{odot}) > 9.44$ at 0.6 $lesssim z lesssim$ 1.2. We have identified authentically quiescent galaxies in the $UVJ$ diagram based on their D4000 strengths. This spectroscopic identification is in good agreement with their photometrically-derived specific star formation rates (sSFR). Morphologically, most (that is, 66 out of 68 galaxies, $sim$ 97 %) of these newly identified quiescent galaxies have a prominent bulge component. However, not all of the bulge-dominated galaxies are quenched. We found that bulge-dominated galaxies show positive correlations among the D4000 strength, stellar mass, and the Sersic index, while late-type disks do not show such strong positive correlations. Also, bulge-dominated galaxies are clearly separated into two main groups in the parameter space of sSFR vs. stellar mass and stellar surface density within the effective radius, $Sigma_{rm e}$, while late-type disks and irregulars only show high sSFR. This split is directly linked to the `blue cloud and the `red sequence populations, and correlates with the associated central compactness indicated by $Sigma_{rm e}$. While star-forming massive late-type disks and irregulars (with D4000 $<$ 1.5 and log$(M_{*}/M_{odot}) gtrsim 10.5$) span a stellar mass range comparable to bulge-dominated galaxies, most have systematically lower $Sigma_{rm e}$ $lesssim$ $10^{9}M_{odot}rm{kpc^{-2}}$. This suggests that the presence of a bulge is a necessary but not sufficient requirement for quenching at intermediate redshifts.
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