The Primordial Inflation Polarization Explorer (PIPER) is a balloon-borne instrument that will probe the epoch of reionization and search for the signature of inflation through large angular scale measurements of the linear polarization of the cosmic microwave background in four frequency bands from 200 to 600 GHz. The PIPER receiver couples two 32x40 arrays of transition-edge sensors (TES) to cryogenic telescope optics. The optics are maintained at < 3 K using superfluid pumps in an open bucket of liquid helium. The receiver houses the detector arrays and sub-K cooler in a superfluid-tight enclosure. We describe several aspects of the receiver design and performance: 1) the thermal design of the receiver and cooling to 100 mK with a continuous adiabatic demagnetization refrigerator (CADR) 2) performance of the TES arrays in the integrated receiver, 3) design of the reimaging optics and superfluid-tight windows. The PIPER receiver is the first implementation of kilo-pixel TES bolometer arrays combined with a continuous ADR operating at 100 mK, which provide 10 uW cooling.