We report a heterodyne receiver using a superconducting NbN hot electron bolometer ͑HEB͒ integrated with a tight winding spiral antenna as mixer and a distributed feedback ͑DFB͒ terahertz quantum cascade laser ͑QCL͒ operating at 3.42 THz as local oscillator. The aim is to demonstrate the readiness of both devices for the detection of OH lines at 3.5 THz in a real instrument. We show that the improved single-spot beam of the terahertz QCL can easily pump the HEB mixer. We measured a double sideband receiver noise temperature of 2100 K at the optimum local oscillator power of 290 nW. This noise temperature can be further reduced to 1100 K if we correct the loss due to the use of an uncoated lens, and the losses of the window and the air. Therefore, the combination of a HEB and such a DFB QCL can in principle be used to detect an OH line at 3.5 THz. However, a high input power of several watts, which is needed to operate the QCL in a liquid-helium cryostat, poses a big challenge to the receiver stability.