We present new Herschel observations of four massive, Sunyaev-Zeldovich Effect (SZE)-selected clusters at $0.3 leq z leq 1.1$, two of which have also been observed with ALMA. We detect 19 Herschel/PACS counterparts to spectroscopically confirmed cluster members, five of which have redshifts determined via CO($4-3$) and [CI](${}^3P_1 - {}^3P_0$) lines. The mean [CI]/CO line ratio is $0.19 pm 0.07$ in brightness temperature units, consistent with previous results for field samples. We do not detect significant stacked ALMA dust continuum or spectral line emission, implying upper limits on mean interstellar medium (H$_2$ + HI) and molecular gas masses. An apparent anticorrelation of $L_{IR}$ with clustercentric radius is driven by the tight relation between star formation rate and stellar mass. We find average specific star formation rate log(sSFR/yr$^{-1}$) = -10.36, which is below the SFR$-M_*$ correlation measured for field galaxies at similar redshifts. The fraction of infrared-bright galaxies (IRBGs; $log (L_{IR}/L_odot) > 10.6$) per cluster and average sSFR rise significantly with redshift. For CO detections, we find $f_{gas} sim 0.2$, comparable to those of field galaxies, and gas depletion timescales of about 2 Gyr. We use radio observations to distinguish active galactic nuclei (AGNs) from star-forming galaxies. At least four of our 19 Herschel cluster members have $q_{IR} < 1.8$, implying an AGN fraction $f_{AGN} gtrsim 0.2$ for our PACS-selected sample.
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